Pub Date : 2025-02-28DOI: 10.1016/j.aim.2025.110169
Renaud Detcherry , Efstratia Kalfagianni , Adam S. Sikora
The proof of Witten's finiteness conjecture established that the Kauffman bracket skein modules of closed 3-manifolds are finitely generated over . In this paper, we develop a novel method for computing these skein modules.
We show that if the skein module of M is tame (e.g. finitely generated over ), and the -character scheme is reduced, then the dimension is the number of closed points in this character scheme. This, in particular, verifies a conjecture in the literature relating to the Abouzaid-Manolescu -Floer theoretic invariants, for infinite families of 3-manifolds.
We prove a criterion for reducedness of character varieties of closed 3-manifolds and use it to compute the skein modules of Dehn fillings of -torus knots and of the figure-eight knot. The later family gives the first instance of computations of skein modules for closed hyperbolic 3-manifolds.
We also prove that the skein modules of rational homology spheres have dimension at least 1 over .
{"title":"Kauffman bracket skein modules of small 3-manifolds","authors":"Renaud Detcherry , Efstratia Kalfagianni , Adam S. Sikora","doi":"10.1016/j.aim.2025.110169","DOIUrl":"10.1016/j.aim.2025.110169","url":null,"abstract":"<div><div>The proof of Witten's finiteness conjecture established that the Kauffman bracket skein modules of closed 3-manifolds are finitely generated over <span><math><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span>. In this paper, we develop a novel method for computing these skein modules.</div><div>We show that if the skein module <span><math><mi>S</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>Q</mi><mo>[</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>±</mo><mn>1</mn></mrow></msup><mo>]</mo><mo>)</mo></math></span> of <em>M</em> is tame (e.g. finitely generated over <span><math><mi>Q</mi><mo>[</mo><msup><mrow><mi>A</mi></mrow><mrow><mo>±</mo><mn>1</mn></mrow></msup><mo>]</mo></math></span>), and the <span><math><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></math></span>-character scheme is reduced, then the dimension <span><math><msub><mrow><mi>dim</mi></mrow><mrow><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msub><mo></mo><mspace></mspace><mi>S</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>)</mo></math></span> is the number of closed points in this character scheme. This, in particular, verifies a conjecture in the literature relating <span><math><msub><mrow><mi>dim</mi></mrow><mrow><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></mrow></msub><mo></mo><mspace></mspace><mi>S</mi><mo>(</mo><mi>M</mi><mo>,</mo><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>)</mo></math></span> to the Abouzaid-Manolescu <span><math><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>C</mi><mo>)</mo></math></span>-Floer theoretic invariants, for infinite families of 3-manifolds.</div><div>We prove a criterion for reducedness of character varieties of closed 3-manifolds and use it to compute the skein modules of Dehn fillings of <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mn>2</mn><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>-torus knots and of the figure-eight knot. The later family gives the first instance of computations of skein modules for closed hyperbolic 3-manifolds.</div><div>We also prove that the skein modules of rational homology spheres have dimension at least 1 over <span><math><mi>Q</mi><mo>(</mo><mi>A</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110169"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143521277","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-28DOI: 10.1016/j.aim.2025.110161
D. Cordero-Erausquin , N. Gozlan , S. Nakamura , H. Tsuji
We reveal the relation between the Legendre transform of convex functions and Heat flow evolution, and how it applies to the functional Blaschke-Santaló inequality. We also describe local maximizers in this inequality.
{"title":"Duality and Heat flow","authors":"D. Cordero-Erausquin , N. Gozlan , S. Nakamura , H. Tsuji","doi":"10.1016/j.aim.2025.110161","DOIUrl":"10.1016/j.aim.2025.110161","url":null,"abstract":"<div><div>We reveal the relation between the Legendre transform of convex functions and Heat flow evolution, and how it applies to the functional Blaschke-Santaló inequality. We also describe local maximizers in this inequality.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110161"},"PeriodicalIF":1.5,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-27DOI: 10.1016/j.aim.2025.110181
Andrei Moroianu , Mihaela Pilca
A conformal product structure on a Riemannian manifold is a Weyl connection with reducible holonomy. We give the geometric description of all compact Kähler manifolds admitting conformal product structures.
{"title":"Conformal product structures on compact Kähler manifolds","authors":"Andrei Moroianu , Mihaela Pilca","doi":"10.1016/j.aim.2025.110181","DOIUrl":"10.1016/j.aim.2025.110181","url":null,"abstract":"<div><div>A conformal product structure on a Riemannian manifold is a Weyl connection with reducible holonomy. We give the geometric description of all compact Kähler manifolds admitting conformal product structures.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110181"},"PeriodicalIF":1.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143510130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-27DOI: 10.1016/j.aim.2025.110182
Omer Ben Neria , Gabriel Goldberg , Eyal Kaplan
We settle a question of Woodin motivated by the philosophy of potentialism in set theory. A sentence in the language of set theory is locally verifiable if it asserts the existence of a level of the cumulative hierarchy of sets with some first-order property; this is equivalent to being in the Lévy hierarchy. A sentence is -satisfiable if it can be forced without changing , and V-satisfiable if it is -satisfiable for all ordinals α. The -Potentialist Principle, introduced by Woodin, asserts that every V-satisfiable locally verifiable sentence is true. We show in Theorem 6.2 that the -Potentialist Principle is consistent relative to a supercompact cardinal. We accomplish this by generalizing Gitik's method of iterating distributive forcings by embedding them into Príkry-type forcings [6, Section 6.4]; our generalization, Theorem 5.2, works for forcings that add no bounded subsets to a strongly compact cardinal, which requires a completely different proof. Finally, using the concept of mutual stationarity, we show in Theorem 7.5 that the -Potentialist Principle implies the consistency of a Woodin cardinal.3
{"title":"The Σ2-Potentialist Principle","authors":"Omer Ben Neria , Gabriel Goldberg , Eyal Kaplan","doi":"10.1016/j.aim.2025.110182","DOIUrl":"10.1016/j.aim.2025.110182","url":null,"abstract":"<div><div>We settle a question of Woodin motivated by the philosophy of potentialism in set theory. A sentence in the language of set theory is <em>locally verifiable</em> if it asserts the existence of a level <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span> of the cumulative hierarchy of sets with some first-order property; this is equivalent to being <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> in the Lévy hierarchy. A sentence is <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span><em>-satisfiable</em> if it can be forced without changing <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>, and <em>V-satisfiable</em> if it is <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>α</mi></mrow></msub></math></span>-satisfiable for all ordinals <em>α</em>. The <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-Potentialist Principle, introduced by Woodin, asserts that every <em>V</em>-satisfiable locally verifiable sentence is true. We show in <span><span>Theorem 6.2</span></span> that the <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-Potentialist Principle is consistent relative to a supercompact cardinal. We accomplish this by generalizing Gitik's method of iterating distributive forcings by embedding them into Príkry-type forcings <span><span>[6, Section 6.4]</span></span>; our generalization, <span><span>Theorem 5.2</span></span>, works for forcings that add no bounded subsets to a strongly compact cardinal, which requires a completely different proof. Finally, using the concept of mutual stationarity, we show in <span><span>Theorem 7.5</span></span> that the <span><math><msub><mrow><mi>Σ</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-Potentialist Principle implies the consistency of a Woodin cardinal.<span><span><sup>3</sup></span></span></div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"467 ","pages":"Article 110182"},"PeriodicalIF":1.5,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-26DOI: 10.1016/j.aim.2025.110170
David Ayala, Aaron Mazel-Gee, Nick Rozenblyum
We undertake a systematic study of the Hochschild homology, i.e. (the geometric realization of) the cyclic nerve, of -categories (and more generally of category-objects in an ∞-category), as a version of factorization homology. In order to do this, we codify -categories in terms of quiver representations in them. By examining a universal instance of such Hochschild homology, we explicitly identify its natural symmetries, and construct a non-stable version of the cyclotomic trace map. Along the way we give a unified account of the cyclic, paracyclic, and epicyclic categories. We also prove that this gives a combinatorial description of the case of factorization homology as presented in [4], which parametrizes -categories by solidly 1-framed stratified spaces.
{"title":"Symmetries of the cyclic nerve","authors":"David Ayala, Aaron Mazel-Gee, Nick Rozenblyum","doi":"10.1016/j.aim.2025.110170","DOIUrl":"10.1016/j.aim.2025.110170","url":null,"abstract":"<div><div>We undertake a systematic study of the Hochschild homology, i.e. (the geometric realization of) the cyclic nerve, of <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-categories (and more generally of category-objects in an ∞-category), as a version of factorization homology. In order to do this, we codify <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-categories in terms of quiver representations in them. By examining a universal instance of such Hochschild homology, we explicitly identify its natural symmetries, and construct a non-stable version of the cyclotomic trace map. Along the way we give a unified account of the cyclic, paracyclic, and epicyclic categories. We also prove that this gives a combinatorial description of the <span><math><mi>n</mi><mo>=</mo><mn>1</mn></math></span> case of factorization homology as presented in <span><span>[4]</span></span>, which parametrizes <span><math><mo>(</mo><mo>∞</mo><mo>,</mo><mn>1</mn><mo>)</mo></math></span>-categories by solidly 1-framed stratified spaces.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"466 ","pages":"Article 110170"},"PeriodicalIF":1.5,"publicationDate":"2025-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-24DOI: 10.1016/j.aim.2025.110156
Fanny Augeri
Let Ξ be the adjacency matrix of an Erdős-Rényi graph on n vertices and with parameter p and consider A a centred random symmetric matrix with bounded i.i.d. entries above the diagonal. When the mean degree np diverges, the empirical spectral measure of the normalized Hadamard product converges weakly in probability to the semicircle law. In the regime where and , we prove a large deviations principle for the empirical spectral measure with speed and with a good rate function solution of a certain variational problem. The rate function reveals in particular that the only possible deviations at the exponential scale are around measures coming from Quadratic Vector Equations. As a byproduct, we obtain a large deviations principle for the empirical spectral measure of supercritical Erdős-Rényi graphs.
{"title":"Large deviations of the empirical spectral measure of supercritical sparse Wigner matrices","authors":"Fanny Augeri","doi":"10.1016/j.aim.2025.110156","DOIUrl":"10.1016/j.aim.2025.110156","url":null,"abstract":"<div><div>Let Ξ be the adjacency matrix of an Erdős-Rényi graph on <em>n</em> vertices and with parameter <em>p</em> and consider <em>A</em> a <span><math><mi>n</mi><mo>×</mo><mi>n</mi></math></span> centred random symmetric matrix with bounded i.i.d. entries above the diagonal. When the mean degree <em>np</em> diverges, the empirical spectral measure of the normalized Hadamard product <span><math><mo>(</mo><mi>A</mi><mo>∘</mo><mi>Ξ</mi><mo>)</mo><mo>/</mo><msqrt><mrow><mi>n</mi><mi>p</mi></mrow></msqrt></math></span> converges weakly in probability to the semicircle law. In the regime where <span><math><mi>p</mi><mo>≪</mo><mn>1</mn></math></span> and <span><math><mi>n</mi><mi>p</mi><mo>≫</mo><mi>log</mi><mo></mo><mi>n</mi></math></span>, we prove a large deviations principle for the empirical spectral measure with speed <span><math><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>p</mi></math></span> and with a good rate function solution of a certain variational problem. The rate function reveals in particular that the only possible deviations at the exponential scale <span><math><msup><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>p</mi></math></span> are around measures coming from Quadratic Vector Equations. As a byproduct, we obtain a large deviations principle for the empirical spectral measure of supercritical Erdős-Rényi graphs.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"466 ","pages":"Article 110156"},"PeriodicalIF":1.5,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143473995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-20DOI: 10.1016/j.aim.2025.110162
Nhat Minh Doan
This paper introduces a natural combinatorial structure of orthogeodesics on hyperbolic surfaces and presents Ptolemy relations among them. As a primary application, we propose a recursive method for computing the trace (the hyperbolic cosine of the length) of orthogeodesics and establish the existence of surfaces where the trace of each orthogeodesic is an integer. These surfaces and their orthogeodesics are closely related to integral Apollonian circle packings. Notably, we found a new type of root-flipping that transitions between roots in different quadratic equations of a certain type, with Vieta root-flipping as a special case. Finally, we provide a combinatorial proof of Basmajian's identity for hyperbolic surfaces, akin to Bowditch's combinatorial proof of the McShane identity.
{"title":"Ortho-integral surfaces","authors":"Nhat Minh Doan","doi":"10.1016/j.aim.2025.110162","DOIUrl":"10.1016/j.aim.2025.110162","url":null,"abstract":"<div><div>This paper introduces a natural combinatorial structure of orthogeodesics on hyperbolic surfaces and presents Ptolemy relations among them. As a primary application, we propose a recursive method for computing the trace (the hyperbolic cosine of the length) of orthogeodesics and establish the existence of surfaces where the trace of each orthogeodesic is an integer. These surfaces and their orthogeodesics are closely related to integral Apollonian circle packings. Notably, we found a new type of root-flipping that transitions between roots in different quadratic equations of a certain type, with Vieta root-flipping as a special case. Finally, we provide a combinatorial proof of Basmajian's identity for hyperbolic surfaces, akin to Bowditch's combinatorial proof of the McShane identity.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"466 ","pages":"Article 110162"},"PeriodicalIF":1.5,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider étale Hausdorff groupoids in which the interior of the isotropy is abelian. We prove that the norms of the images under regular representations, of elements of the reduced groupoid -algebra whose supports are contained in the interior of the isotropy vary upper semicontinuously. This corrects an error in [2].
{"title":"Norm upper-semicontinuity of functions supported on open abelian isotropy in étale groupoids. Corrigendum to “Reconstruction of groupoids and C⁎-rigidity of dynamical systems” [Adv. Math. 390 (2021) 107923]","authors":"Toke Meier Carlsen , Anna Duwenig , Efren Ruiz , Aidan Sims","doi":"10.1016/j.aim.2025.110150","DOIUrl":"10.1016/j.aim.2025.110150","url":null,"abstract":"<div><div>We consider étale Hausdorff groupoids in which the interior of the isotropy is abelian. We prove that the norms of the images under regular representations, of elements of the reduced groupoid <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra whose supports are contained in the interior of the isotropy vary upper semicontinuously. This corrects an error in <span><span>[2]</span></span>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"466 ","pages":"Article 110150"},"PeriodicalIF":1.5,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-19DOI: 10.1016/j.aim.2025.110147
Claudia Alfes , Jens Funke , Michael H. Mertens , Eugenia Rosu
We construct harmonic weak Maass forms that map to cusp forms of weight with rational coefficients under the ξ-operator. This generalizes work of the first author, Griffin, Ono, and Rolen, who constructed distinguished preimages under this differential operator of weight 2 newforms associated to rational elliptic curves using the classical Weierstrass theory of elliptic functions. We extend this theory and construct a vector-valued Jacobi–Weierstrass ζ-function which is a generalization of the classical Weierstrass ζ-function.
{"title":"On Jacobi–Weierstrass mock modular forms","authors":"Claudia Alfes , Jens Funke , Michael H. Mertens , Eugenia Rosu","doi":"10.1016/j.aim.2025.110147","DOIUrl":"10.1016/j.aim.2025.110147","url":null,"abstract":"<div><div>We construct harmonic weak Maass forms that map to cusp forms of weight <span><math><mi>k</mi><mo>≥</mo><mn>2</mn></math></span> with rational coefficients under the <em>ξ</em>-operator. This generalizes work of the first author, Griffin, Ono, and Rolen, who constructed distinguished preimages under this differential operator of weight 2 newforms associated to rational elliptic curves using the classical Weierstrass theory of elliptic functions. We extend this theory and construct a vector-valued Jacobi–Weierstrass <em>ζ</em>-function which is a generalization of the classical Weierstrass <em>ζ</em>-function.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"465 ","pages":"Article 110147"},"PeriodicalIF":1.5,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143444701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-19DOI: 10.1016/j.aim.2025.110158
Anna Roig-Sanchis
We study the length spectrum of a model of random hyperbolic 3-manifolds introduced in [31]. These are compact manifolds with boundary constructed by randomly gluing truncated tetrahedra along their faces. We prove that, as the volume tends to infinity, their length spectrum converge in distribution to a Poisson point process on , with computable intensity λ.
{"title":"The length spectrum of random hyperbolic 3-manifolds","authors":"Anna Roig-Sanchis","doi":"10.1016/j.aim.2025.110158","DOIUrl":"10.1016/j.aim.2025.110158","url":null,"abstract":"<div><div>We study the length spectrum of a model of random hyperbolic 3-manifolds introduced in <span><span>[31]</span></span>. These are compact manifolds with boundary constructed by randomly gluing truncated tetrahedra along their faces. We prove that, as the volume tends to infinity, their length spectrum converge in distribution to a Poisson point process on <span><math><msub><mrow><mi>R</mi></mrow><mrow><mo>></mo><mn>0</mn></mrow></msub></math></span>, with computable intensity <em>λ</em>.</div></div>","PeriodicalId":50860,"journal":{"name":"Advances in Mathematics","volume":"466 ","pages":"Article 110158"},"PeriodicalIF":1.5,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143436516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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