Geometry & Topology

Right-veering diffeomorphisms of compact surfaces with boundary II

Ko Honda, William H Kazez, and Gordana Matić

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We continue our study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary, introduced in [Invent. Math. 169 (2007) 427–449]. We conduct a detailed study of the case when the surface is a punctured torus; in particular, we exhibit the difference between the monoid of right-veering diffeomorphisms and the monoid of products of positive Dehn twists, with the help of the Rademacher function. We then generalize to the braid group Bn on n strands by relating the signature and the Maslov index. Finally, we discuss the symplectic fillability in the pseudo-Anosov case by comparing with the work of Roberts [Proc. London Math. Soc. (3) 82/83 (2001) 747–768/443–471].

Article information

Geom. Topol., Volume 12, Number 4 (2008), 2057-2094.

Received: 6 December 2006
Revised: 22 April 2008
Accepted: 18 June 2008
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)

tight contact structure bypass open book decomposition fibered link mapping class group Dehn twists


Honda, Ko; Kazez, William H; Matić, Gordana. Right-veering diffeomorphisms of compact surfaces with boundary II. Geom. Topol. 12 (2008), no. 4, 2057--2094. doi:10.2140/gt.2008.12.2057.

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