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

Dahmani, François

doi:10.2140/gt.2018.22.4113

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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

DOI: 10.2140/gt.2018.22.4113

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

Volume 22, issue 7 (2018)