Right-veering diffeomorphisms of compact surfaces with boundary II

Details Right-veering diffeomorphisms of compact surfaces with boundary II Right-veering diffeomorphisms of compact surfaces with boundary II

2006-03-27

arxiv.org/abs/math/0603626v2

Mathematics

Geometric Topology

25 pages, 5 figures

Scientific paper

10.1007/s00222-007-0051-4

We continue our study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary, introduced in [HKM2]. 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 [Ro1,Ro2].

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