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Asymptotically rigid
mapping class groups, I: Finiteness properties of braided
Thompson's and Houghton's groups
Anthony Genevois, Anne Lonjou and Christian Urech |
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Geometry & Topology 26 (2022) 1385–1434
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Abstract |
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We study the asymptotically rigid mapping class groups of infinitely punctured surfaces obtained by thickening planar trees. Such groups include the braided Ptolemy–Thompson groups introduced by Funar and Kapoudjian, and the braided Houghton groups introduced by Degenhardt. We present an elementary construction of a contractible cube complex, on which these groups act with cube stabilizers isomorphic to finite extensions of braid groups. As an application, we prove conjectures of Funar–Kapoudjian and Degenhardt by showing that and are of type and that is of type but not of type . |
Keywords
Thompson groups, Houghton groups, braid groups, big mapping
class groups, asymptotically rigid mapping class groups,
cube complexes
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Mathematical Subject Classification
Primary: 20F65
Secondary: 20J05
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References |
Publication
Received: 28 October 2020
Revised: 21 December 2020
Accepted: 21 January 2021
Published: 3 August 2022
Proposed: Mladen Bestvina
Seconded: David M Fisher, Anna Wienhard
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Authors |
| Anthony Genevois | |
| Institut Montpelliérain Alexander
Grothendieck Université de Montpellier Montpellier France |
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| Anne Lonjou | |
| Département de Mathématiques Faculté des Sciences d’Orsay Université Paris-Saclay Orsay France |
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| Christian Urech | |
| Institut de Mathématiques École Polytechniqe Fédérale de Lausanne Lausanne Switzerland |
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