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Factorizations of diffeomorphisms of compact surfaces with boundary

Andy Wand
Geometry & Topology 19 (2015) 2407–2464
DOI: 10.2140/gt.2015.19.2407
Abstract

We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of being right-veering. We use these to construct open book decompositions of Stein-fillable 3–manifolds whose monodromies have no positive factorization.

Keywords
contact structures, open book decompositions, mapping class groups, Stein fillings
Mathematical Subject Classification 2010
Primary: 57R17
References
Publication
Received: 9 October 2009
Revised: 3 October 2012
Accepted: 5 January 2015
Published: 20 October 2015
Proposed: Danny Calegari
Seconded: Dmitri Burago, Peter S. Ozsváth
Authors
Andy Wand
Laboratoire de Mathématiques Jean Leray
Université de Nantes
2, rue de la Houssinière
44322 Nantes
France