发布求助
文献互助 智能选刊 最新文献

Pure and Applied Mathematics Quarterly最新文献

筛选
英文 中文
Any oriented non-closed connected $4$-manifold can be spread holomorphically over the complex projective plane minus a point 任何定向的非封闭连通 $4$-manifold 都可以在复投影面上全形展开，减去一个点
IF 0.7 4区 数学
Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI: 10.4310/pamq.2023.v19.n6.a11
Dennis Sullivan
{"title":"Any oriented non-closed connected $4$-manifold can be spread holomorphically over the complex projective plane minus a point","authors":"Dennis Sullivan","doi":"10.4310/pamq.2023.v19.n6.a11","DOIUrl":"https://doi.org/10.4310/pamq.2023.v19.n6.a11","url":null,"abstract":"$defspinc{operatorname{spin}^mathrm{c}}$We give a 1965 era proof of the title assuming $M$ is $spinc$. The fact that any oriented four manifold is $spinc$ is a challenging result from 1995 whose interesting argument by Teichner–Vogt is analyzed and used in the appendix to show an analogous integral lift result about the top Wu class in $dim 4k$. This will be used in future work to study related complex structures on higher dimensional open manifolds.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139659454","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}
引用次数: 0
Spectral measures for $Sp(2)$ Sp(2)$的谱测量
IF 0.7 4区 数学
Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI: 10.4310/pamq.2023.v19.n5.a1
David Evans, Mathew Pugh
{"title":"Spectral measures for $Sp(2)$","authors":"David Evans, Mathew Pugh","doi":"10.4310/pamq.2023.v19.n5.a1","DOIUrl":"https://doi.org/10.4310/pamq.2023.v19.n5.a1","url":null,"abstract":"Spectral measures provide invariants for braided subfactors via fusion modules. In this paper we study joint spectral measures associated to the compact connected rank two Lie group $SO(5)$ and its double cover the compact connected, simply-connected rank two Lie group $Sp(2)$, including the McKay graphs for the irreducible representations of $Sp(2)$ and $SO(5)$ and their maximal tori, and fusion modules associated to the $Sp(2)$ modular invariants.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647312","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}
引用次数: 0
Curvature in the balance: the Weyl functional and scalar curvature of $4$-manifolds 平衡中的曲率：韦尔函数和 $4$-manifolds 的标量曲率
IF 0.7 4区 数学
Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI: 10.4310/pamq.2023.v19.n6.a5
Claude LeBrun
{"title":"Curvature in the balance: the Weyl functional and scalar curvature of $4$-manifolds","authors":"Claude LeBrun","doi":"10.4310/pamq.2023.v19.n6.a5","DOIUrl":"https://doi.org/10.4310/pamq.2023.v19.n6.a5","url":null,"abstract":"The infimum of the Weyl functional is shown to be surprisingly small on many compact $4$-manifolds that admit positive-scalar-curvature metrics. Results are also proved that systematically compare the scalar and self-dual Weyl curvatures of certain almost-Kähler $4$-manifolds.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139656351","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}
引用次数: 0
Graded extensions of generalized Haagerup categories 广义哈格鲁普范畴的梯度扩展
IF 0.7 4区 数学
Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI: 10.4310/pamq.2023.v19.n5.a3
Pinhas Grossman, Masaki Izumi, Noah Snyder
{"title":"Graded extensions of generalized Haagerup categories","authors":"Pinhas Grossman, Masaki Izumi, Noah Snyder","doi":"10.4310/pamq.2023.v19.n5.a3","DOIUrl":"https://doi.org/10.4310/pamq.2023.v19.n5.a3","url":null,"abstract":"$defZ{mathbb{Z}}$We classify certain $Z_2$-graded extensions of generalized Haagerup categories in terms of numerical invariants satisfying polynomial equations. In particular, we construct a number of new examples of fusion categories, including: $Z_2$-graded extensions of $Z_{2n}$ generalized Haagerup categories for all $n leq 5$; $Z_2 times Z_2$-graded extensions of the Asaeda-Haagerup categories; and extensions of the $Z_2 times Z_2$ generalized Haagerup category by its outer automorphism group $A_4$. The construction uses endomorphism categories of operator algebras, and in particular, free products of Cuntz algebras with free group $mathrm{C}^ast$-algebras.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647537","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}
引用次数: 0
Interplay between nonlinear potential theory and fully nonlinear elliptic PDEs 非线性势理论与全非线性椭圆 PDE 之间的相互作用
IF 0.7 4区 数学
Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI: 10.4310/pamq.2023.v19.n6.a14
F. Reese Harvey, Kevin R. Payne
{"title":"Interplay between nonlinear potential theory and fully nonlinear elliptic PDEs","authors":"F. Reese Harvey, Kevin R. Payne","doi":"10.4310/pamq.2023.v19.n6.a14","DOIUrl":"https://doi.org/10.4310/pamq.2023.v19.n6.a14","url":null,"abstract":"We discuss one of the many topics that illustrate the interaction of Blaine Lawson’s deep geometric and analytic insights. The first author is extremely grateful to have had the pleasure of collaborating with Blaine over many enjoyable years. The topic to be discussed concerns the fruitful interplay between <i>nonlinear potential theory</i>; that is, the study of subharmonics with respect to a general constraint set in the $2$-jet bundle and the study of subsolutions and supersolutions of a nonlinear (degenerate) elliptic PDE. The main results include (but are not limited to) the validity of the comparison principle and the existence and uniqueness to solutions to the relevant Dirichlet problems on domains which are suitably “pseudoconvex”. The methods employed are geometric and flexible as well as being very general on the potential theory side, which is interesting in its own right. Moreover, in many important geometric contexts no natural operator may be present. On the other hand, the potential theoretic approach can yield results on the PDE side in terms of non standard structural conditions on a given differential operator.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139656344","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}
引用次数: 0
$RO(C_2)$-graded equivariant cohomology and classical Steenrod squares RO(C_2)级等变同构与经典斯泰恩罗德方阵
IF 0.7 4区 数学
Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI: 10.4310/pamq.2023.v19.n6.a7
Pedro F. dos Santos, Paulo Lima-Filho
{"title":"$RO(C_2)$-graded equivariant cohomology and classical Steenrod squares","authors":"Pedro F. dos Santos, Paulo Lima-Filho","doi":"10.4310/pamq.2023.v19.n6.a7","DOIUrl":"https://doi.org/10.4310/pamq.2023.v19.n6.a7","url":null,"abstract":"We investigate the <i>restriction to fixed-points</i> and <i>change of coefficient functors</i> in $RO(C_2)$-graded equivariant cohomology, with applications to the equivariant cohomology of spaces with a trivial $C_2$-action for $underline{mathbb{Z}}$ and $underline{mathbb{F}_2}$ coefficients. To this end, we study the nonequivariant spectra representing these theories and the corresponding functors. In particular, we show that the $RO(C2)$-graded homology class determined by a Real submanifold $Y$ (in the sense of Atiyah) of a Real compact manifold $X$ encodes the total Steenrod square of the dual to $Y^{C_2}$ in $X^{C_2}$.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139656214","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}
引用次数: 0
Positive scalar curvature on manifolds with boundary and their doubles 有边界流形上的正标量曲率及其倍数
IF 0.7 4区 数学
Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI: 10.4310/pamq.2023.v19.n6.a12
Jonathan Rosenberg, Shmuel Weinberger
{"title":"Positive scalar curvature on manifolds with boundary and their doubles","authors":"Jonathan Rosenberg, Shmuel Weinberger","doi":"10.4310/pamq.2023.v19.n6.a12","DOIUrl":"https://doi.org/10.4310/pamq.2023.v19.n6.a12","url":null,"abstract":"This paper is about positive scalar curvature on a compact manifold $X$ with non-empty boundary $partial X$. In some cases, we completely answer the question of when $X$ has a positive scalar curvature metric which is a product metric near $partial X$, or when $X$ has a positive scalar curvature metric with positive mean curvature on the boundary, and more generally, we study the relationship between boundary conditions on $partial X$ for positive scalar curvature metrics on $X$ and the positive scalar curvature problem for the double $M = operatorname{Dbl} (X, partial X)$.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139656311","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}
引用次数: 0
A remark on calibrations and Lie groups 关于定标和李群的评论
IF 0.7 4区 数学
Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI: 10.4310/pamq.2023.v19.n6.a2
Nigel Hitchin
{"title":"A remark on calibrations and Lie groups","authors":"Nigel Hitchin","doi":"10.4310/pamq.2023.v19.n6.a2","DOIUrl":"https://doi.org/10.4310/pamq.2023.v19.n6.a2","url":null,"abstract":"We use the notion of the principal three-dimensional subgroup of a simple Lie group to identify certain special subspaces of the Lie algebra and address the question of whether these are calibrated for invariant forms on the group.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139656317","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}
引用次数: 0
A note on continuous entropy 关于连续熵的说明
IF 0.7 4区 数学
Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI: 10.4310/pamq.2023.v19.n5.a5
Roberto Longo, Edward Witten
{"title":"A note on continuous entropy","authors":"Roberto Longo, Edward Witten","doi":"10.4310/pamq.2023.v19.n5.a5","DOIUrl":"https://doi.org/10.4310/pamq.2023.v19.n5.a5","url":null,"abstract":"Von Neumann entropy has a natural extension to the case of an arbitrary semifinite von Neumann algebra, as was considered by I. E. Segal. We relate this entropy to the relative entropy and show that the entropy increase for an inclusion of von Neumann factors is bounded by the logarithm of the Jones index. The bound is optimal if the factors are infinite dimensional.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647268","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}
引用次数: 0
Spin Calogero-Moser periodic chains and two dimensional Yang-Mills theory with corners 自旋卡洛吉罗-莫泽周期链和带角的二维杨-米尔斯理论
IF 0.7 4区 数学
Pure and Applied Mathematics Quarterly Pub Date : 2024-01-30 DOI: 10.4310/pamq.2023.v19.n5.a7
Nicolai Reshetikhin
{"title":"Spin Calogero-Moser periodic chains and two dimensional Yang-Mills theory with corners","authors":"Nicolai Reshetikhin","doi":"10.4310/pamq.2023.v19.n5.a7","DOIUrl":"https://doi.org/10.4310/pamq.2023.v19.n5.a7","url":null,"abstract":"The Quantum Calogero–Moser spin system is a superintegrable system with the spectrum of commuting Hamiltonians that can be described entirely in terms of representation theory of the corresponding simple Lie group. Here we describe its natural generalization known as quantum Calogero–Moser spin chain or $N$-spin Calogero–Moser system. In the first part of this paper we show that quantum Calogero–Moser spin chain is a quantum superintegrable systems. Then we show that the Euclidean multi-time propagator for this model can be written as a partition function of a two-dimensional Yang–Mills theory on a cylinder. Then we argue that the two-dimensional Yang–Mills theory withWilson loops with “outer ends” should be regarded as the theory on space times with non-removable corners. Partition functions of such theory satisfy non-stationary Calogero–Moser equations. In this paper the underlying Lie group $G$ is a compact connected, simply connected simple Lie group.","PeriodicalId":54526,"journal":{"name":"Pure and Applied Mathematics Quarterly","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139647269","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}
引用次数: 0
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信