{"title":"四曲面的悬浮及其应用","authors":"Tseleung So, Stephen Theriault","doi":"10.1007/s11856-024-2659-0","DOIUrl":null,"url":null,"abstract":"<p>Let <i>M</i> be a smooth, orientable, closed, connected 4-manifold and suppose that <i>H</i><sub>1</sub>(<i>M</i>; ℤ) is finitely generated and has no 2-torsion. We give a homotopy decomposition of the suspension of <i>M</i> in terms of spheres, Moore spaces and Σℂ<i>P</i><sup>2</sup>. This is used to calculate any reduced generalized cohomology theory of <i>M</i> as a group and to determine the homotopy types of certain current groups and gauge groups.</p>","PeriodicalId":14661,"journal":{"name":"Israel Journal of Mathematics","volume":"19 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The suspension of a 4-manifold and its applications\",\"authors\":\"Tseleung So, Stephen Theriault\",\"doi\":\"10.1007/s11856-024-2659-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <i>M</i> be a smooth, orientable, closed, connected 4-manifold and suppose that <i>H</i><sub>1</sub>(<i>M</i>; ℤ) is finitely generated and has no 2-torsion. We give a homotopy decomposition of the suspension of <i>M</i> in terms of spheres, Moore spaces and Σℂ<i>P</i><sup>2</sup>. This is used to calculate any reduced generalized cohomology theory of <i>M</i> as a group and to determine the homotopy types of certain current groups and gauge groups.</p>\",\"PeriodicalId\":14661,\"journal\":{\"name\":\"Israel Journal of Mathematics\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Israel Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11856-024-2659-0\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Israel Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11856-024-2659-0","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
设 M 是光滑、可定向、封闭、连通的 4-manifold，并假设 H1(M; ℤ)是有限生成的且无 2-扭转。我们用球面、摩尔空间和 ΣℂP2 给出了 M 的悬浮同调分解。我们用它来计算 M 作为一个群的任何还原广义同调理论，并确定某些流群和规群的同调类型。
The suspension of a 4-manifold and its applications
Let M be a smooth, orientable, closed, connected 4-manifold and suppose that H1(M; ℤ) is finitely generated and has no 2-torsion. We give a homotopy decomposition of the suspension of M in terms of spheres, Moore spaces and ΣℂP2. This is used to calculate any reduced generalized cohomology theory of M as a group and to determine the homotopy types of certain current groups and gauge groups.
期刊介绍：
The Israel Journal of Mathematics is an international journal publishing high-quality original research papers in a wide spectrum of pure and applied mathematics. The prestigious interdisciplinary editorial board reflects the diversity of subjects covered in this journal, including set theory, model theory, algebra, group theory, number theory, analysis, functional analysis, ergodic theory, algebraic topology, geometry, combinatorics, theoretical computer science, mathematical physics, and applied mathematics.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
