Advances in Mathematics最新文献

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The constant term algebra of type A: The structure

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-02-18 DOI: 10.1016/j.aim.2025.110154

Guoce Xin , Chen Zhang , Yue Zhou , Yueming Zhong

In this paper, we discover a new noncommutative algebra. We refer this algebra as the constant term algebra of type A, which is generated by certain constant term operators. We characterize a structural result of this algebra by establishing an explicit basis in terms of certain forests. This algebra arises when we apply the method of the iterated Laurent series to investigate Beck and Pixton's residue computation for the Ehrhart series of the Birkhoff polytope. This algebra seems to be the first structural result in the area of the constant term world since the discovery of the Dyson constant term identity in 1962.

引用次数: 0

An adjunction inequality for the Bauer–Furuta type invariants, with applications to sliceness and 4-manifold topology

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-02-18 DOI: 10.1016/j.aim.2025.110134

Nobuo Iida , Anubhav Mukherjee , Masaki Taniguchi

Our main result gives an adjunction inequality for embedded surfaces in certain 4-manifolds with contact boundary under a non-vanishing assumption on the Bauer–Furuta type invariants. Using this, we give infinitely many knots in

S^{3}

that are not smoothly H-slice (that is, bounding a null-homologous disk) in many 4-manifolds but they are topologically H-slice. In particular, we give such knots in the boundaries of the punctured elliptic surfaces

E (2 n)

. In addition, we give obstructions to codimension-0 orientation-reversing embedding of weak symplectic fillings with

b_{3} = 0

into closed symplectic 4-manifolds with

b_{1} = 0

and

b_{2}^{+} \equiv 3 \mod 4

. From here we prove a Bennequin type inequality for strong symplectic caps of

(S^{3}, ξ_{s t d})

. We also show that any weakly symplectically fillable 3-manifold bounds a 4-manifold with at least two smooth structures.

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引用次数: 0

Ergodic measures of intermediate entropies for dynamical systems with the approximate product property

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-02-18 DOI: 10.1016/j.aim.2025.110159

Peng Sun

For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structure of the space of invariant measures: The ergodic measures of intermediate entropies and the ones of intermediate pressures are generic in certain subspaces. Consequently, the conjecture of Katok that ergodic measures of arbitrary intermediate entropy exist is verified for a broad class of systems.

引用次数: 0

An extended Hilbert scale and its applications

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-02-18 DOI: 10.1016/j.aim.2025.110155

Vladimir Mikhailets , Aleksandr Murach , Tetiana Zinchenko

We propose a new viewpoint on Hilbert scales extending them by means of all Hilbert spaces that are interpolation ones between spaces on the scale. We prove that this extension admits an explicit description with the help of OR-varying functions of the operator generating the scale. We also show that this extended Hilbert scale is obtained by the quadratic interpolation (with function parameter) between the above spaces and is closed with respect to the quadratic interpolation between Hilbert spaces. We give applications of the extended Hilbert scale to interpolational inequalities, generalized Sobolev spaces, and spectral expansions induced by abstract and elliptic operators; this specifically allows obtaining new results for multiple Fourier series.

引用次数: 0

A non-mixing Arnold flow on a surface

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-02-17 DOI: 10.1016/j.aim.2025.110157

Bassam Fayad, Adam Kanigowski, Rigoberto Zelada

We construct a smooth area preserving flow on a genus 2 surface with exactly one open uniquely ergodic component, that is asymmetrically bounded by separatrices of non-degenerate saddles and that is nevertheless not mixing.

引用次数: 0

Irrationality of the general smooth quartic 3-fold using intermediate Jacobians

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-02-14 DOI: 10.1016/j.aim.2025.110160

Benson Farb

We prove that the intermediate Jacobian of the Klein quartic 3-fold X is not isomorphic, as a principally polarized abelian variety, to a product of Jacobians of curves. As corollaries we deduce (using a criterion of Clemens-Griffiths) that X, as well as the general smooth quartic 3-fold, is irrational. These corollaries were known: Iskovskih-Manin [14] proved that every smooth quartic 3-fold is irrational. However, the method of proof here is different than that of [14], is significantly simpler, and produces an explicit example.

引用次数: 0

Equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-02-14 DOI: 10.1016/j.aim.2025.110153

Yuta Takaya

We prove the equidimensionality of affine Deligne-Lusztig varieties in mixed characteristic. This verifies a conjecture made by Rapoport and implies that the results of Nie and Zhou-Zhu can be extended to the whole irreducible components of affine Deligne-Lusztig varieties. The method is to translate the work of Hartl-Viehmann into mixed characteristic and construct local foliations for affine Deligne-Lusztig varieties. This leads us to develop a theory of formal algebraic geometry for perfect schemes.

引用次数: 0

Quillen cohomology of enriched operads

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-02-14 DOI: 10.1016/j.aim.2025.110151

Truong Hoang

A modern insight due to Quillen, which is further developed by Lurie, asserts that many cohomology theories of interest are particular cases of a single construction, which allows one to define cohomology groups in an abstract setting using only intrinsic properties of the category (or ∞-category) at hand. This universal cohomology theory is known as Quillen cohomology. In any setting, Quillen cohomology of a given object is classified by its cotangent complex. The main purpose of this paper is to study Quillen cohomology of operads enriched over a general base category. Our main result provides an explicit formula for computing Quillen cohomology of enriched operads, based on a procedure of taking certain infinitesimal models of their cotangent complexes. Furthermore, we propose a natural construction of the twisted arrow ∞-categories of simplicial operads. We then assert that the cotangent complex of a simplicial operad can be represented as a spectrum valued functor on its twisted arrow ∞-category.

When working in stable base categories such as chain complexes and spectra, Francis and Lurie proved the existence of a fiber sequence relating the cotangent complex and Hochschild complex of an

E_{n}

-algebra, from which a conjecture of Kontsevich is verified. We establish an analogous fiber sequence for the operad

E_{n}

itself, in the topological setting.

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引用次数: 0

The classification of vertex operator algebras of OZ-type generated by Ising vectors of σ-type 由σ型伊辛向量生成的OZ型顶点算子代数的分类

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-02-14 DOI: 10.1016/j.aim.2025.110146

Cuipo Jiang , Ching Hung Lam , Hiroshi Yamauchi

We classify vertex operator algebras (VOAs) of OZ-type generated by Ising vectors of σ-type. As a consequence of the classification, we also prove that such VOAs are simple, rational,

C_{2}

-cofinite and unitary, that is, they have compact real forms generated by Ising vectors of σ-type over the real numbers.

引用次数: 0

Skein and cluster algebras of unpunctured surfaces for sp4

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics

Pub Date : 2025-02-13 DOI: 10.1016/j.aim.2025.110149

Tsukasa Ishibashi , Wataru Yuasa

As a sequel to our previous work [18] on the

{sl}_{3}

-case, we introduce a skein algebra

S_{{sp}_{4}, Σ}^{q}

consisting of

{sp}_{4}

-webs on a marked surface Σ, incorporating certain “clasped” skein relations at special points. We further investigate its cluster structure. We also define a natural

Z_{q}

-form

S_{{sp}_{4}, Σ}^{Z_{q}} \subset S_{{sp}_{4}, Σ}^{q}

, while the natural coefficient ring

R

S_{{sp}_{4}, Σ}^{q}

includes the inverse of the quantum integer

{[2]}_{q}

. We prove that its boundary-localization

S_{{sp}_{4}, Σ}^{Z_{q}} [\partial^{- 1}]

embeds into a quantum cluster algebra

A_{{sp}_{4}, Σ}^{q}

that quantizes the function ring of the moduli space

A_{S p_{4}, Σ}^{\times}

. Furthermore, we establish the positivity of Laurent expressions of elevation-preserving webs, following an approach similar to [18]. We also propose a characterization of cluster variables in the spirit of Fomin–Pylyavskyy [9] using

{sp}_{4}

-webs, and provide infinitely many supporting examples on a quadrilateral.

引用次数: 0

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