大映射类群同调中的紧和有限型支持

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-08-28 DOI:10.1112/jlms.70258

Martin Palmer, Xiaolei Wu

{"title":"大映射类群同调中的紧和有限型支持","authors":"Martin Palmer, Xiaolei Wu","doi":"10.1112/jlms.70258","DOIUrl":null,"url":null,"abstract":"For any infinite-type surface <math>\n <semantics>\n <mi>S</mi>\n <annotation>$S$</annotation>\n </semantics></math>, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface; or (ii) a finite-type subsurface. Our purpose here is to study this question, in particular giving an almost-complete answer when the genus of <math>\n <semantics>\n <mi>S</mi>\n <annotation>$S$</annotation>\n </semantics></math> is positive (including infinite) and a partial answer when the genus of <math>\n <semantics>\n <mi>S</mi>\n <annotation>$S$</annotation>\n </semantics></math> is zero. Our methods involve the notion of shiftable subsurfaces as well as homological stability for mapping class groups of finite-type surfaces.","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 3","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70258","citationCount":"0","resultStr":"{\"title\":\"Compact and finite-type support in the homology of big mapping class groups\",\"authors\":\"Martin Palmer, Xiaolei Wu\",\"doi\":\"10.1112/jlms.70258\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For any infinite-type surface <math>\\n <semantics>\\n <mi>S</mi>\\n <annotation>$S$</annotation>\\n </semantics></math>, a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface; or (ii) a finite-type subsurface. Our purpose here is to study this question, in particular giving an almost-complete answer when the genus of <math>\\n <semantics>\\n <mi>S</mi>\\n <annotation>$S$</annotation>\\n </semantics></math> is positive (including infinite) and a partial answer when the genus of <math>\\n <semantics>\\n <mi>S</mi>\\n <annotation>$S$</annotation>\\n </semantics></math> is zero. Our methods involve the notion of shiftable subsurfaces as well as homological stability for mapping class groups of finite-type surfaces.\",\"PeriodicalId\":49989,\"journal\":{\"name\":\"Journal of the London Mathematical Society-Second Series\",\"volume\":\"112 3\",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70258\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the London Mathematical Society-Second Series\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70258\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70258","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

对于任意无限型曲面S$ S$，一个很自然的问题是：它的映射类群的同调是否包含在(i)紧次曲面上支持的非平凡类；或（ii）有限型地下。我们的目的是研究这个问题，特别是给出S$ S$的属为正（包括无穷）时的几乎完全答案和S$ S$的属为零时的部分答案。我们的方法涉及可移子曲面的概念以及有限型曲面映射类群的同调稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Compact and finite-type support in the homology of big mapping class groups

查看原文本刊更多论文

Compact and finite-type support in the homology of big mapping class groups

For any infinite-type surface $S$ , a natural question is whether the homology of its mapping class group contains any non-trivial classes that are supported on (i) a compact subsurface; or (ii) a finite-type subsurface. Our purpose here is to study this question, in particular giving an almost-complete answer when the genus of $S$ is positive (including infinite) and a partial answer when the genus of $S$ is zero. Our methods involve the notion of shiftable subsurfaces as well as homological stability for mapping class groups of finite-type surfaces.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.