{"title":"A mass transportation proof of the sharp one-dimensional Gagliardo–Nirenberg inequalities","authors":"V. H. Nguyen","doi":"10.2969/jmsj/82258225","DOIUrl":"https://doi.org/10.2969/jmsj/82258225","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49035489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Extremal trigonal fibrations on rational surfaces","authors":"C. Gong, S. Kitagawa, Jun Lu","doi":"10.2969/jmsj/82438243","DOIUrl":"https://doi.org/10.2969/jmsj/82438243","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41402088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For any compact riemannian surface of genus three $(Sigma,ds^2)$ Yang and Yau proved that the product of the first eigenvalue of the Laplacian $lambda_1(ds^2)$ and the area $Area(ds^2)$ is bounded above by $24pi$. In this paper we improve the result and we show that $lambda_1(ds^2)Area(ds^2)leq16(4-sqrt{7})pi approx 21.668,pi$. About the sharpness of the bound, for the hyperbolic Klein quartic surface numerical computations give the value $approx 21.414,pi$.
{"title":"On the first eigenvalue of the Laplacian on compact surfaces of genus three","authors":"A. Ros","doi":"10.2969/jmsj/85898589","DOIUrl":"https://doi.org/10.2969/jmsj/85898589","url":null,"abstract":"For any compact riemannian surface of genus three $(Sigma,ds^2)$ Yang and Yau proved that the product of the first eigenvalue of the Laplacian $lambda_1(ds^2)$ and the area $Area(ds^2)$ is bounded above by $24pi$. In this paper we improve the result and we show that $lambda_1(ds^2)Area(ds^2)leq16(4-sqrt{7})pi approx 21.668,pi$. About the sharpness of the bound, for the hyperbolic Klein quartic surface numerical computations give the value $approx 21.414,pi$.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45167362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We prove categorical systolic inequalities for the derived categories of 2-Calabi-Yau Ginzburg dg algebras associated to ADE quivers and explore their symplecto-geometric aspects.
{"title":"Systolic inequalities, Ginzburg dg algebras and Milnor fibers","authors":"Jongmyeong Kim","doi":"10.2969/jmsj/85878587","DOIUrl":"https://doi.org/10.2969/jmsj/85878587","url":null,"abstract":"We prove categorical systolic inequalities for the derived categories of 2-Calabi-Yau Ginzburg dg algebras associated to ADE quivers and explore their symplecto-geometric aspects.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47069698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
For an abelian group $ A $, we study a close connection between braided crossed $ A $-categories with a trivialization of the $ A $-action and $ A $-graded braided tensor categories. Additionally, we prove that the obstruction to the existence of a trivialization of a categorical group action $T$ on a monoidal category $mathcal{C}$ is given by an element $O(T)in H^2(G,operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}}))$. In the case that $O(T)=0$, the set of obstructions form a torsor over $operatorname{Hom}(G,operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}}))$, where $operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}})$ is the abelian group of tensor natural automorphisms of the identity. The cohomological interpretation of trivializations, together with the homotopical classification of (faithfully graded) braided $A$-crossed tensor categories developed in arXiv:0909.3140, allows us to provide a method for the construction of faithfully $A$-graded braided tensor categories. We work out two examples. First, we compute the obstruction to the existence of trivializations for the braided crossed category associated with a pointed semisimple tensor category. In the second example, we compute explicit formulas for the braided $mathbb{Z}/2$-crossed structures over Tambara-Yamagami fusion categories and, consequently, a conceptual interpretation of the results in arXiv:math/0011037 about the classification of braidings over Tambara-Yamagami categories.
对于阿贝尔群$ A $，我们研究了$ A $-作用和$ A $-分级编织张量范畴之间的紧密联系。此外，我们证明了一元范畴$mathcal{C}$上的范畴群作用$T$的平凡化存在的障碍是由H^2(G，operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}}) $中的元素$O(T)给出的。在$O(T)=0$的情况下，障碍物集合在$operatorname{hm}(G，operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}}))$上形成一个torsor，其中$operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}})$是单位元的张量自然自同构的阿贝尔群。平凡化的上同解释，以及arXiv:0909.3140中提出的(忠实分级)编织A交叉张量范畴的同局部分类，使我们能够提供一种构造忠实A分级编织张量范畴的方法。我们算出两个例子。首先，我们计算了与点半简单张量范畴相关的编织交叉范畴的琐屑化存在的障碍。在第二个例子中，我们计算了Tambara-Yamagami融合范畴上编织的$mathbb{Z}/2$-交叉结构的显式公式，从而对arXiv:math/0011037中关于Tambara-Yamagami范畴上编织分类的结果进行了概念解释。
{"title":"Trivializing group actions on braided crossed tensor categories and graded braided tensor categories","authors":"César Galindo","doi":"10.2969/jmsj/85768576","DOIUrl":"https://doi.org/10.2969/jmsj/85768576","url":null,"abstract":"For an abelian group $ A $, we study a close connection between braided crossed $ A $-categories with a trivialization of the $ A $-action and $ A $-graded braided tensor categories. Additionally, we prove that the obstruction to the existence of a trivialization of a categorical group action $T$ on a monoidal category $mathcal{C}$ is given by an element $O(T)in H^2(G,operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}}))$. In the case that $O(T)=0$, the set of obstructions form a torsor over $operatorname{Hom}(G,operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}}))$, where $operatorname{Aut}_otimes(operatorname{Id}_{mathcal{C}})$ is the abelian group of tensor natural automorphisms of the identity. \u0000The cohomological interpretation of trivializations, together with the homotopical classification of (faithfully graded) braided $A$-crossed tensor categories developed in arXiv:0909.3140, allows us to provide a method for the construction of faithfully $A$-graded braided tensor categories. We work out two examples. First, we compute the obstruction to the existence of trivializations for the braided crossed category associated with a pointed semisimple tensor category. In the second example, we compute explicit formulas for the braided $mathbb{Z}/2$-crossed structures over Tambara-Yamagami fusion categories and, consequently, a conceptual interpretation of the results in arXiv:math/0011037 about the classification of braidings over Tambara-Yamagami categories.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43538658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Poincaré inequalities with exact missing terms on homogeneous groups","authors":"T. Ozawa, D. Suragan","doi":"10.2969/jmsj/83738373","DOIUrl":"https://doi.org/10.2969/jmsj/83738373","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47752995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maciej Borodzik, Przemysław Grabowski, A. Krol, Maria Marchwicka
{"title":"Linking forms, finite orthogonal groups and periodicity of links","authors":"Maciej Borodzik, Przemysław Grabowski, A. Krol, Maria Marchwicka","doi":"10.2969/jmsj/82028202","DOIUrl":"https://doi.org/10.2969/jmsj/82028202","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"72 1","pages":"1025-1048"},"PeriodicalIF":0.7,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47421757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. '. L'opez, Ram'on Barral Lij'o, O. Lukina, Hiraku Nozawa
The discriminant group of a minimal equicontinuous action of a group $G$ on a Cantor set $X$ is the subgroup of the closure of the action in the group of homeomorphisms of $X$, consisting of homeomorphisms which fix a given point. The stabilizer and the centralizer groups associated to the action are obtained as direct limits of sequences of subgroups of the discriminant group with certain properties. Minimal equicontinuous group actions on Cantor sets admit a classification by the properties of the stabilizer and centralizer direct limit groups. In this paper, we construct new families of examples of minimal equicontinuous actions on Cantor sets, which illustrate certain aspects of this classification. These examples are constructed as actions on rooted trees. The acting groups are countable subgroups of the product or of the wreath product of groups. We discuss applications of our results to the study of attractors of dynamical systems and of minimal sets of foliations.
{"title":"Wild Cantor actions","authors":"J. '. L'opez, Ram'on Barral Lij'o, O. Lukina, Hiraku Nozawa","doi":"10.2969/JMSJ/85748574","DOIUrl":"https://doi.org/10.2969/JMSJ/85748574","url":null,"abstract":"The discriminant group of a minimal equicontinuous action of a group $G$ on a Cantor set $X$ is the subgroup of the closure of the action in the group of homeomorphisms of $X$, consisting of homeomorphisms which fix a given point. The stabilizer and the centralizer groups associated to the action are obtained as direct limits of sequences of subgroups of the discriminant group with certain properties. Minimal equicontinuous group actions on Cantor sets admit a classification by the properties of the stabilizer and centralizer direct limit groups. \u0000In this paper, we construct new families of examples of minimal equicontinuous actions on Cantor sets, which illustrate certain aspects of this classification. These examples are constructed as actions on rooted trees. The acting groups are countable subgroups of the product or of the wreath product of groups. We discuss applications of our results to the study of attractors of dynamical systems and of minimal sets of foliations.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":" ","pages":""},"PeriodicalIF":0.7,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46988360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Construction of spectra of triangulated categories and applications to commutative rings","authors":"H. Matsui, Ryo Takahashi","doi":"10.2969/jmsj/82868286","DOIUrl":"https://doi.org/10.2969/jmsj/82868286","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"72 1","pages":"1283-1307"},"PeriodicalIF":0.7,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49209302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Automorphism groups of smooth cubic threefolds","authors":"Li Wei, Xun Yu","doi":"10.2969/jmsj/83088308","DOIUrl":"https://doi.org/10.2969/jmsj/83088308","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":"72 1","pages":"1327-1343"},"PeriodicalIF":0.7,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45434945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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