Hierarchically cocompact classifying spaces for mapping class groups of surfaces
Hierarchically cocompact classifying spaces for mapping class groups of surfaces
We define the notion of a hierarchically cocompact classifying space for a family of subgroups of a group. Our main application is to show that the mapping class group Mod ( S ) of any connected oriented compact surface S , possibly with punctures and boundary components and with negative Euler characteristic has a hierarchically cocompact model for the family of virtually cyclic subgroups of dimension at most vcd Mod ( S ) + 1 . When the surface is closed, we prove that this bound is optimal. In particular, this answers a question of Lück for mapping class groups of surfaces.
1-14
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Nucinkis, Brita E.
ab19ea83-d78f-44ec-8e81-aca9bd580a0d
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6
Nucinkis, Brita E.
ab19ea83-d78f-44ec-8e81-aca9bd580a0d
Petrosyan, Nansen and Nucinkis, Brita E.
(2018)
Hierarchically cocompact classifying spaces for mapping class groups of surfaces.
Bulletin of the London Mathematical Society, .
(doi:10.1112/blms.12166).
Abstract
We define the notion of a hierarchically cocompact classifying space for a family of subgroups of a group. Our main application is to show that the mapping class group Mod ( S ) of any connected oriented compact surface S , possibly with punctures and boundary components and with negative Euler characteristic has a hierarchically cocompact model for the family of virtually cyclic subgroups of dimension at most vcd Mod ( S ) + 1 . When the surface is closed, we prove that this bound is optimal. In particular, this answers a question of Lück for mapping class groups of surfaces.
Text
hierarchical_F_final
- Author's Original
Restricted to Repository staff only
Request a copy
Text
hierarchical_F_final
- Accepted Manuscript
More information
Accepted/In Press date: 20 April 2018
e-pub ahead of print date: 14 May 2018
Identifiers
Local EPrints ID: 420131
URI: http://eprints.soton.ac.uk/id/eprint/420131
ISSN: 0024-6093
PURE UUID: ca4ef0cd-cd44-4cdb-982f-c01080b39e6b
Catalogue record
Date deposited: 27 Apr 2018 16:30
Last modified: 16 Mar 2024 04:17
Export record
Altmetrics
Contributors
Author:
Brita E. Nucinkis
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
