#### Volume 12, issue 4 (2008)

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Right-veering diffeomorphisms of compact surfaces with boundary II

### Ko Honda, William H Kazez and Gordana Matić

Geometry & Topology 12 (2008) 2057–2094
##### Abstract

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 ${B}_{n}$ 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].

##### Keywords
tight, contact structure, bypass, open book decomposition, fibered link, mapping class group, Dehn twists
Primary: 57M50
Secondary: 53C15