Right-veering diffeomorphisms of compact surfaces with boundary

Abstract

We continue our study of the monoid of right-veering diffeomorphisms on a\ncompact oriented surface with nonempty boundary, introduced in [HKM2]. We\nconduct a detailed study of the case when the surface is a punctured torus; in\nparticular, we exhibit the difference between the monoid of right-veering\ndiffeomorphisms and the monoid of products of positive Dehn twists, with the\nhelp of the Rademacher function. We then generalize to the braid group B_n on n\nstrands by relating the signature and the Maslov index. Finally, we discuss the\nsymplectic fillability in the pseudo-Anosov case by comparing with the work of\nRoberts [Ro1,Ro2].\n