Groups with exotic finiteness properties from complex Morse theory

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2025-02-28 DOI:10.1112/topo.70013

Claudio Llosa Isenrich, Pierre Py

{"title":"Groups with exotic finiteness properties from complex Morse theory","authors":"Claudio Llosa Isenrich, Pierre Py","doi":"10.1112/topo.70013","DOIUrl":null,"url":null,"abstract":"Recent constructions have shown that interesting behaviours can be observed in the finiteness properties of Kähler groups and their subgroups. In this work, we push this further and exhibit, for each integer <math>\n <semantics>\n <mi>k</mi>\n <annotation>$k$</annotation>\n </semantics></math>, new hyperbolic groups admitting surjective homomorphisms to <math>\n <semantics>\n <mi>Z</mi>\n <annotation>${\\mathbb {Z}}$</annotation>\n </semantics></math> and to <math>\n <semantics>\n <msup>\n <mi>Z</mi>\n <mn>2</mn>\n </msup>\n <annotation>${\\mathbb {Z}}^{2}$</annotation>\n </semantics></math>, whose kernel is of type <math>\n <semantics>\n <msub>\n <mi>F</mi>\n <mi>k</mi>\n </msub>\n <annotation>$\\mathcal {F}_{k}$</annotation>\n </semantics></math> but not of type <math>\n <semantics>\n <msub>\n <mi>F</mi>\n <mrow>\n <mi>k</mi>\n <mo>+</mo>\n <mn>1</mn>\n </mrow>\n </msub>\n <annotation>$\\mathcal {F}_{k+1}$</annotation>\n </semantics></math>. By a fibre product construction, we also find examples of non-normal subgroups of Kähler groups with exotic finiteness properties.","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"18 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.70013","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.70013","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

Abstract

Recent constructions have shown that interesting behaviours can be observed in the finiteness properties of Kähler groups and their subgroups. In this work, we push this further and exhibit, for each integer $k$ , new hyperbolic groups admitting surjective homomorphisms to $Z$ and to $Z^{2}$ , whose kernel is of type $F_{k}$ but not of type $F_{k + 1}$ . By a fibre product construction, we also find examples of non-normal subgroups of Kähler groups with exotic finiteness properties.

Abstract Image

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.