Work

Asymptotically rigid mapping class groups III: Presentations and isomorphisms

Year: 2025

Type: preprint

Abstract: This article is dedicated to the computation of an explicit presentation of some asymptotically rigid mapping class groups, namely the braided Higman-Thompson groups. To do so, we use the action of these groups on the spine complex, a simply connected cube complex constructed by the authors in a previous work. In particular, this allows to compute the abelianisations of these groups. With these new algebraic invariants we can handle many new cases of the isomorphism problem for asymptotically rigid mapping class groups of trees.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2510.11336

Authors: Genevois, Anthony, Lonjou, Anne, Urech, Christian

Institutions: Université de Montpellier, Institut Montpelliérain Alexander Grothendieck, Laboratoire de Mathématiques d'Orsay, ETH Zurich

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung, Agencia Estatal de Investigación

Awards: G1175115578, G2262748287, G300979063, G3480869486, G3654024709, The geometry of groups of birational transformations, G4084979677, G425668148, Groups acting on fractals, G5080475149, G6625153282

OpenAlex ID: W4416008756

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