Simplicial structures and normal forms for mapping class groups and braid groups

Berrick, A J; Hanbury, E

doi:10.2140/agt.2014.14.3259

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Simplicial structures and normal forms for mapping class groups and braid groups

A J Berrick and E Hanbury

Algebraic & Geometric Topology 14 (2014) 3259–3280

DOI: 10.2140/agt.2014.14.3259

Abstract

In this paper we show that the mapping class groups of any surface with nonempty boundary form a simplicial group as the number of marked points varies. This extends the simplicial structure on braid groups of surfaces found by Berrick, Cohen, Wong and Wu. We use the simplicial maps to construct compatible normal forms for elements of the braid groups and mapping class groups of surfaces with boundary.

Keywords

braid group, mapping class group, configuration space, crossed simplicial group, combing, normal form

Mathematical Subject Classification 2010

Primary: 20F38

Secondary: 20E22, 55U10

References

Publication

Received: 23 November 2012

Revised: 2 February 2014

Accepted: 6 February 2014

Published: 15 January 2015

Authors

A J Berrick
Yale-NUS College 6 College Avenue East #B1-01 Singapore 138614 Singapore

E Hanbury
Department of Mathematics University of Durham Science Laboratories Durham DH1 3LE UK

Volume 14, issue 6 (2014)