{"title":"poincar<s:1>对偶群的弦拓扑","authors":"Hossein Abbaspour, R. Cohen, Kate Gruher","doi":"10.2140/gtm.2008.13.1","DOIUrl":null,"url":null,"abstract":"where the sum is taken over conjugacy classes of elements in G . In this paper we construct a multiplication on LG directly in terms of intersection products on the centralizers. This multiplication makes LG a graded, associative, commutative algebra. When G is the fundamental group of an aspherical, closed oriented n‐ manifold M , then .LG/ D HC n.LM/, where LM is the free loop space of M . We show that the product on LG corresponds to the string topology loop product on H .LM/ defined by Chas and Sullivan. 55P35; 20J06 Dedicated to Fred Cohen on the occasion of his 60th birthday","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"81 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2005-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":"{\"title\":\"String topology of Poincaré duality groups\",\"authors\":\"Hossein Abbaspour, R. Cohen, Kate Gruher\",\"doi\":\"10.2140/gtm.2008.13.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"where the sum is taken over conjugacy classes of elements in G . In this paper we construct a multiplication on LG directly in terms of intersection products on the centralizers. This multiplication makes LG a graded, associative, commutative algebra. When G is the fundamental group of an aspherical, closed oriented n‐ manifold M , then .LG/ D HC n.LM/, where LM is the free loop space of M . We show that the product on LG corresponds to the string topology loop product on H .LM/ defined by Chas and Sullivan. 55P35; 20J06 Dedicated to Fred Cohen on the occasion of his 60th birthday\",\"PeriodicalId\":115248,\"journal\":{\"name\":\"Geometry and Topology Monographs\",\"volume\":\"81 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2005-11-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry and Topology Monographs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/gtm.2008.13.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry and Topology Monographs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gtm.2008.13.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
摘要
对G中元素的共轭类求和。在本文中，我们直接构造了一个LG上的乘法，它是由中心点上的交积构成的。这个乘法使LG成为一个分级的，结合能交换的代数。当G是一个非球面闭合定向n流形M的基群时，则。lg / D HC n.LM/，其中LM为M的自由环空间。我们证明了LG上的乘积对应于Chas和Sullivan. 55P35定义的H . lm /上的弦拓扑环积;20J06在弗雷德·科恩60岁生日之际献给他
where the sum is taken over conjugacy classes of elements in G . In this paper we construct a multiplication on LG directly in terms of intersection products on the centralizers. This multiplication makes LG a graded, associative, commutative algebra. When G is the fundamental group of an aspherical, closed oriented n‐ manifold M , then .LG/ D HC n.LM/, where LM is the free loop space of M . We show that the product on LG corresponds to the string topology loop product on H .LM/ defined by Chas and Sullivan. 55P35; 20J06 Dedicated to Fred Cohen on the occasion of his 60th birthday
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