Mathematische Zeitschrift最新文献_第4页

Central elements in the $$textrm{SL}_d$$ -skein algebra of a surface 曲面的 $$textrm{SL}_d$ -skein 代数中的中心元

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-26 DOI: 10.1007/s00209-024-03559-9

Francis Bonahon, Vijay Higgins

引用次数: 0

The mod 2 cohomology rings of oriented Grassmannians via Koszul complexes 通过科斯祖尔复数的定向格拉斯曼的模 2 同调环

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-26 DOI: 10.1007/s00209-024-03556-y

Ákos K. Matszangosz, Matthias Wendt

{"title":"The mod 2 cohomology rings of oriented Grassmannians via Koszul complexes","authors":"Ákos K. Matszangosz, Matthias Wendt","doi":"10.1007/s00209-024-03556-y","DOIUrl":"https://doi.org/10.1007/s00209-024-03556-y","url":null,"abstract":"We study the structure of mod 2 cohomology rings of oriented Grassmannians (widetilde{{text {Gr}}}_k(n)) of oriented k-planes in ({mathbb {R}}^n). Our main focus is on the structure of the cohomology ring (textrm{H}^*(widetilde{{text {Gr}}}_k(n);{mathbb {F}}_2)) as a module over the characteristic subring C, which is the subring generated by the Stiefel–Whitney classes (w_2,ldots ,w_k). We identify this module structure using Koszul complexes, which involves the syzygies between the relations defining C. We give an infinite family of such syzygies, which results in a new upper bound on the characteristic rank of (widetilde{{text {Gr}}}_k(2^t)), (k<2^t), and formulate a conjecture on the exact value of the characteristic rank of (widetilde{{text {Gr}}}_k(n)). For the case (k=3), we use the Koszul complex to compute a presentation of the cohomology ring (H=textrm{H}^*(widetilde{{text {Gr}}}_3(n);{mathbb {F}}_2)) for (2^{t-1}<nle 2^t-4) for (tge 4), complementing existing descriptions in the cases (n=2^t-i), (i=0,1,2,3) for (tge 3). More precisely, as a C-module, H splits as a direct sum of the characteristic subring C and the anomalous module H/C, and we compute a complete presentation of H/C as a C-module from the Koszul complex. We also discuss various issues that arise for the cases (k>3), supported by computer calculation.","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"46 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141784981","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Comparing orthogonal calculus and calculus with Reality 正交微积分与现实微积分的比较

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-22 DOI: 10.1007/s00209-024-03545-1

Niall Taggart

引用次数: 0

Enumeration of non-nodal real plane rational curves 非节点实平面有理曲线枚举

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-20 DOI: 10.1007/s00209-024-03546-0

Eugenii Shustin

引用次数: 0

Mutations of numerically exceptional collections on surfaces 表面上数字特殊集合的变异

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-15 DOI: 10.1007/s00209-024-03550-4

Johannes Krah

引用次数: 0

Optimal quantitative stability for a Serrin-type problem in convex cones 凸锥体中塞林型问题的最佳定量稳定性

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-15 DOI: 10.1007/s00209-024-03555-z

Filomena Pacella, Giorgio Poggesi, Alberto Roncoroni

引用次数: 0

Toric periods for a p-adic quaternion algebra p-adic 四元数代数的 Toric 周期

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-14 DOI: 10.1007/s00209-024-03551-3

U. K. Anandavardhanan, Basudev Pattanayak

{"title":"Toric periods for a p-adic quaternion algebra","authors":"U. K. Anandavardhanan, Basudev Pattanayak","doi":"10.1007/s00209-024-03551-3","DOIUrl":"https://doi.org/10.1007/s00209-024-03551-3","url":null,"abstract":"Let G be a compact group with two given subgroups H and K. Let (pi ) be an irreducible representation of G such that its space of H-invariant vectors as well as the space of K-invariant vectors are both one dimensional. Let (v_H) (resp. (v_K)) denote an H-invariant (resp. K-invariant) vector of unit norm in a given G-invariant inner product (langle ~,~ rangle _pi ) on (pi ). We are interested in calculating the correlation coefficient $$begin{aligned} c(pi text {;},H,K) = |langle v_H,v_K rangle _pi |^2. end{aligned}$$In this paper, we compute the correlation coefficient of an irreducible representation of the multiplicative group of the p-adic quaternion algebra with respect to any two tori. In particular, if (pi ) is such an irreducible representation of odd minimal conductor with non-trivial invariant vectors for two tori H and K, then its root number (varepsilon (pi )) is (pm 1) and (c(pi text {;}, H, K)) is non-vanishing precisely when (varepsilon (pi ) = 1).","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"41 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141613804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exotic families of symplectic manifolds with Milnor fibers of ADE-type 具有 ADE 型米尔诺纤维的奇异交点流形族

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-12 DOI: 10.1007/s00209-024-03542-4

Dongwook Choa, Dogancan Karabas, Sangjin Lee

引用次数: 0

Topological Hecke eigenforms 拓扑对冲特征形式

IF 0.8 3区数学

Mathematische Zeitschrift Pub Date : 2024-07-12 DOI: 10.1007/s00209-024-03552-2

L. Candelori, A. Salch

引用次数: 0

Parametrizations of subsets of the space of valuations 估值空间子集的参数化