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Non-commutative Barge-Ghys Quasimorphisms 非交换的巴杰-盖斯准变形
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-30 DOI: 10.1093/imrn/rnae119
Michael Brandenbursky, Misha Verbitsky
{"title":"Non-commutative Barge-Ghys Quasimorphisms","authors":"Michael Brandenbursky, Misha Verbitsky","doi":"10.1093/imrn/rnae119","DOIUrl":"https://doi.org/10.1093/imrn/rnae119","url":null,"abstract":"A (non-commutative) Ulam quasimorphism is a map $q$ from a group $Gamma $ to a topological group $G$ such that $q(xy)q(y)^{-1}q(x)^{-1}$ belongs to a fixed compact subset of $G$. Generalizing the construction of Barge and Ghys, we build a family of quasimorphisms on a fundamental group of a closed manifold $M$ of negative sectional curvature, taking values in an arbitrary Lie group. This construction, which generalizes the Barge-Ghys quasimorphisms, associates a quasimorphism to any principal $G$-bundle with connection on $M$. Kapovich and Fujiwara have shown that all quasimorphisms taking values in a discrete group can be constructed from group homomorphisms and quasimorphisms taking values in a commutative group. We construct Barge-Ghys type quasimorphisms taking prescribed values on a given subset in $Gamma $, producing counterexamples to the Kapovich and Fujiwara theorem for quasimorphisms taking values in a Lie group. Our construction also generalizes a result proven by D. Kazhdan in his paper “On $varepsilon $-representations”. Kazhdan has proved that for any $varepsilon>0$, there exists an $varepsilon $-representation of the fundamental group of a Riemann surface of genus 2 which cannot be $1/10$-approximated by a representation. We generalize his result by constructing an $varepsilon $-representation of the fundamental group of a closed manifold of negative sectional curvature taking values in an arbitrary Lie group.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Actions of Compact and Discrete Quantum Groups on Operator Systems 紧凑与离散量子群在算子系统上的作用
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-30 DOI: 10.1093/imrn/rnae118
Joeri De Ro, Lucas Hataishi
{"title":"Actions of Compact and Discrete Quantum Groups on Operator Systems","authors":"Joeri De Ro, Lucas Hataishi","doi":"10.1093/imrn/rnae118","DOIUrl":"https://doi.org/10.1093/imrn/rnae118","url":null,"abstract":"We introduce the notion of an action of a discrete or compact quantum group on an operator system, and study equivariant operator system injectivity. We then prove a duality result that relates equivariant injectivity with dual injectivity of associated crossed products. As an application, we give a description of the equivariant injective envelope of the reduced crossed product built from an action of a discrete quantum group on an operator system.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
The Endoscopic Classification of Representations of Non-Quasi-Split Odd Special Orthogonal Groups 非准分裂奇数特殊正交群表征的内窥镜分类
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-29 DOI: 10.1093/imrn/rnae113
Hiroshi Ishimoto
{"title":"The Endoscopic Classification of Representations of Non-Quasi-Split Odd Special Orthogonal Groups","authors":"Hiroshi Ishimoto","doi":"10.1093/imrn/rnae113","DOIUrl":"https://doi.org/10.1093/imrn/rnae113","url":null,"abstract":"In an earlier book of Arthur, the endoscopic classification of representations of quasi-split orthogonal and symplectic groups was established. Later Mok gave that of quasi-split unitary groups. After that, Kaletha, Minguez, Shin, and White gave that of non-quasi-split unitary groups for generic parameters. In this paper we prove the endoscopic classification of representations of non-quasi-split odd special orthogonal groups for generic parameters, following Kaletha, Minguez, Shin, and White.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141190959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
On a Theorem of Lafforgue 论拉弗尔格的一个定理
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-29 DOI: 10.1093/imrn/rnae114
Matthew Baker, Oliver Lorscheid
{"title":"On a Theorem of Lafforgue","authors":"Matthew Baker, Oliver Lorscheid","doi":"10.1093/imrn/rnae114","DOIUrl":"https://doi.org/10.1093/imrn/rnae114","url":null,"abstract":"We give a new proof, along with some generalizations, of a folklore theorem (attributed to Laurent Lafforgue) that a rigid matroid (i.e., a matroid with indecomposable basis polytope) has only finitely many projective equivalence classes of representations over any given field.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
On Symplectic Birational Self-Maps of Projective Hyperkähler Manifolds of K3$^{[n]}$-Type 论K3$^{[n]}$型投影超凯勒积分的交映双理自映射
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-29 DOI: 10.1093/imrn/rnae112
Yajnaseni Dutta, Dominique Mattei, Yulieth Prieto-Montañez
{"title":"On Symplectic Birational Self-Maps of Projective Hyperkähler Manifolds of K3$^{[n]}$-Type","authors":"Yajnaseni Dutta, Dominique Mattei, Yulieth Prieto-Montañez","doi":"10.1093/imrn/rnae112","DOIUrl":"https://doi.org/10.1093/imrn/rnae112","url":null,"abstract":"We prove that projective hyperkähler manifolds of K3$^{[n]}$-type admitting a non-trivial symplectic birational self-map of finite order are isomorphic to moduli spaces of stable (twisted) coherent sheaves on K3 surfaces. Motivated by this result, we analyze the reflections on the movable cone of moduli spaces of sheaves and determine when they come from a birational involution.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141191124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Full Exceptional Collections and Stability Conditions for Dynkin Quivers Dynkin Quivers 的完整异常集合和稳定性条件
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-27 DOI: 10.1093/imrn/rnae110
Takumi Otani
{"title":"Full Exceptional Collections and Stability Conditions for Dynkin Quivers","authors":"Takumi Otani","doi":"10.1093/imrn/rnae110","DOIUrl":"https://doi.org/10.1093/imrn/rnae110","url":null,"abstract":"For a stability condition $sigma $ on a triangulated category, Dimitrov–Katzarkov introduced the notion of a $sigma $-exceptional collection. In this paper, we study full $sigma $-exceptional collections in the derived category of an acyclic quiver. In particular, we prove that any stability condition $sigma $ on the derived category of a Dynkin quiver admits a full $sigma $-exceptional collection.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141169733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Singular Vortex Pairs Follow Magnetic Geodesics 奇异涡旋对遵循磁性大地线
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-23 DOI: 10.1093/imrn/rnae106
Theodore D Drivas, Daniil Glukhovskiy, Boris Khesin
{"title":"Singular Vortex Pairs Follow Magnetic Geodesics","authors":"Theodore D Drivas, Daniil Glukhovskiy, Boris Khesin","doi":"10.1093/imrn/rnae106","DOIUrl":"https://doi.org/10.1093/imrn/rnae106","url":null,"abstract":"We consider pairs of point vortices having circulations $Gamma _{1}$ and $Gamma _{2}$ and confined to a two-dimensional surface $S$. In the limit of zero initial separation $varepsilon $, we prove that they follow a magnetic geodesic in unison, if properly renormalized. Specifically, the “singular vortex pair” moves as a single-charged particle on the surface with a charge of order $1/varepsilon ^{2}$ in an magnetic field $B$ that is everywhere normal to the surface and of strength $|B|=Gamma _{1} +Gamma _{2}$. In the case $Gamma _{1}=-Gamma _{2}$, this gives another proof of Kimura’s conjecture [11] that singular dipoles follow geodesics.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
A Generalization of Operads Based on Subgraph Contractions 基于子图收缩的 Operads 广义
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-23 DOI: 10.1093/imrn/rnae096
Denis Lyskov
{"title":"A Generalization of Operads Based on Subgraph Contractions","authors":"Denis Lyskov","doi":"10.1093/imrn/rnae096","DOIUrl":"https://doi.org/10.1093/imrn/rnae096","url":null,"abstract":"We introduce a generalization of the notion of operad that we call a contractad, whose set of operations is indexed by connected graphs and whose composition rules are numbered by contractions of connected subgraphs. We show that many classical operads, such as the operad of commutative algebras, Lie algebras, associative algebras, pre-Lie algebras, the little disks operad, and the operad of moduli spaces of stable curves $operatorname{overline{{mathcal{M}}}}_{0,n+1}$, admit generalizations to contractads. We explain that standard tools like Koszul duality and the machinery of Gröbner bases can be easily generalized to contractads. We verify the Koszul property of the commutative, Lie, associative, and Gerstenhaber contractads.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153040","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
The Dimension of the Set of $psi $-Badly Approximable Points in All Ambient Dimensions: On a Question of Beresnevich and Velani 在所有环境维度中$psi$坏近似点集合的维度：关于别列斯涅维奇和维拉尼的一个问题
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-22 DOI: 10.1093/imrn/rnae101
Henna Koivusalo, Jason Levesley, Benjamin Ward, Xintian Zhang
{"title":"The Dimension of the Set of $psi $-Badly Approximable Points in All Ambient Dimensions: On a Question of Beresnevich and Velani","authors":"Henna Koivusalo, Jason Levesley, Benjamin Ward, Xintian Zhang","doi":"10.1093/imrn/rnae101","DOIUrl":"https://doi.org/10.1093/imrn/rnae101","url":null,"abstract":"Let $psi :{mathbb{N}} to [0,infty )$, $psi (q)=q^{-(1+tau )}$ and let $psi $-badly approximable points be those vectors in ${mathbb{R}}^{d}$ that are $psi $-well approximable, but not $cpsi $-well approximable for arbitrarily small constants $c>0$. We establish that the $psi $-badly approximable points have the Hausdorff dimension of the $psi $-well approximable points, the dimension taking the value $(d+1)/(tau +1)$ familiar from theorems of Besicovitch and Jarník. The method of proof is an entirely new take on the Mass Transference Principle (MTP) by Beresnevich and Velani (Annals, 2006); namely, we use the colloquially named “delayed pruning” to construct a sufficiently large $liminf $ set and combine this with ideas inspired by the proof of the MTP to find a large $limsup $ subset of the $liminf $ set. Our results are a generalisation of some $1$-dimensional results due to Bugeaud and Moreira (Acta Arith, 2011), but our method of proof is nothing alike.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
On a Generalization of Symmetric Edge Polytopes to Regular Matroids 论对称边多边形对正则表达式的泛化
IF 1 2区 数学
International Mathematics Research Notices Pub Date : 2024-05-22 DOI: 10.1093/imrn/rnae107
Alessio D’Alì, Martina Juhnke-Kubitzke, Melissa Koch
{"title":"On a Generalization of Symmetric Edge Polytopes to Regular Matroids","authors":"Alessio D’Alì, Martina Juhnke-Kubitzke, Melissa Koch","doi":"10.1093/imrn/rnae107","DOIUrl":"https://doi.org/10.1093/imrn/rnae107","url":null,"abstract":"Starting from any finite simple graph, one can build a reflexive polytope known as a symmetric edge polytope. The first goal of this paper is to show that symmetric edge polytopes are intrinsically matroidal objects: more precisely, we prove that two symmetric edge polytopes are unimodularly equivalent precisely when they share the same graphical matroid. The second goal is to show that one can construct a generalized symmetric edge polytope starting from every regular matroid. Just like in the usual case, we are able to find combinatorial ways to describe the facets and an explicit regular unimodular triangulation of any such polytope. Finally, we show that the Ehrhart theory of the polar of a given generalized symmetric edge polytope is tightly linked to the structure of the lattice of flows of the dual regular matroid.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
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