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The normal closure of big Dehn twists and plate spinning with rotating families

François Dahmani

Geometry & Topology 22 (2018) 4113–4144
Abstract

We study the normal closure of a big power of one or several Dehn twists in a mapping class group. We prove that it has a presentation whose relators consist only of commutators between twists of disjoint support, thus answering a question of Ivanov. Our method is to use the theory of projection complexes of Bestvina, Bromberg and Fujiwara, together with the theory of rotating families, simultaneously on several spaces.

Keywords
Dehn twist, mapping class group, rotating families, projection complexes
Mathematical Subject Classification 2010
Primary: 20E07, 20F65
References
Publication
Received: 5 May 2017
Revised: 28 March 2018
Accepted: 30 April 2018
Published: 6 December 2018
Proposed: Ian Agol
Seconded: Dmitri Burago, Peter Teichner
Authors
François Dahmani
Institut Fourier
Université Grenoble Alpes
Grenoble
France