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  Linear groups, conjugacy growth, and classifying spaces for families of subgroups

Puttkamer, T. v., & Wu, X. (2019). Linear groups, conjugacy growth, and classifying spaces for families of subgroups. International Mathematics Research Notices, 2019(10), 3130-3168. doi:10.1093/imrn/rnx215.

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 Creators:
Puttkamer, Timm von1, Author           
Wu, Xiaolei1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Group Theory, Algebraic Topology
 Abstract: Given a group $G$ and a family of subgroups $\mathcal{F}$, we consider its
classifying space $E_{\mathcal F}G$ with respect to $\mathcal{F}$. When
$\mathcal F = \mathcal{VC}yc$ is the family of virtually cyclic subgroups, Juan-Pineda and Leary conjectured that a group admits a finite model for this classifying space if and only if it is virtually cyclic. By establishing a connection to conjugacy growth we can show that this conjecture holds for linear groups. We investigate a similar question that was asked by Lück-Reich-Rognes-Varisco for the family of cyclic subgroups. Finally, we construct finitely generated groups that exhibit wild inner automorphims but which admit a model for $E_{\mathcal{VC}yc}(G)$ whose 0-skeleton is finite.

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Language(s): eng - English
 Dates: 2019
 Publication Status: Issued
 Pages: 39
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Degree: -

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Title: International Mathematics Research Notices
  Abbreviation : IMRN
Source Genre: Journal
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Publ. Info: Oxford University Press
Pages: - Volume / Issue: 2019 (10) Sequence Number: - Start / End Page: 3130 - 3168 Identifier: -