Geometry & Topology

Factorizations of diffeomorphisms of compact surfaces with boundary

Andy Wand

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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.

Article information

Geom. Topol., Volume 19, Number 5 (2015), 2407-2464.

Received: 9 October 2009
Revised: 3 October 2012
Accepted: 5 January 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology

contact structures open book decompositions mapping class groups Stein fillings


Wand, Andy. Factorizations of diffeomorphisms of compact surfaces with boundary. Geom. Topol. 19 (2015), no. 5, 2407--2464. doi:10.2140/gt.2015.19.2407.

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