Rightveering diffeomorphisms of compact surfaces with boundary II

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 Bn on n strands by relating the signature and the Maslov index. Finally, we discuss the symplectic fillability in the pseudoAnosov case by comparing with the work of Roberts. © 2008 Mathematical Sciences Publishers.