Multitwists in big mapping class groups

Domat, George; Fanoni, Federica; Hensel, Sebastian

doi:10.2140/agt.2025.25.3921

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ISSN (electronic): 1472-2739

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Multitwists in big mapping class groups

George Domat, Federica Fanoni and Sebastian Hensel

Algebraic & Geometric Topology 25 (2025) 3921–3929

DOI: 10.2140/agt.2025.25.3921

Abstract

We show that the group generated by multitwists (ie products of powers of twists about disjoint nonaccumulating curves) doesn’t contain the Torelli group of an infinite-type surface. As a consequence, multitwists don’t generate the closure of the compactly supported mapping class group of a surface of infinite type.

Keywords

big mapping class groups, infinite-type surfaces, multitwists

Mathematical Subject Classification

Primary: 20F65, 57K20

References

Publication

Received: 10 March 2023

Revised: 23 July 2024

Accepted: 19 August 2024

Published: 29 October 2025

Authors

George Domat
University of Michigan Department of Mathematics Ann Arbor, MI United States

Federica Fanoni
Laboratoire d’Analyse et de Mathématiques Appliqueées Université Paris-Est Créteil Val de Marne Créteil France

Sebastian Hensel
Department Mathematisches Institut LMU München Munich Germany

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Volume 25, issue 7 (2025)