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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

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].

tight, contact structure, bypass, open book decomposition, fibered link, mapping class group, Dehn twists
Mathematical Subject Classification 2000
Primary: 57M50
Secondary: 53C15
Received: 6 December 2006
Revised: 22 April 2008
Accepted: 18 June 2008
Published: 26 July 2008
Proposed: Yasha Eliashberg
Seconded: Peter Ozsváth, Tom Mrowka
Ko Honda
Department of Mathematics
University of Southern California
Los Angeles
CA 90089
http://rcf.usc.edu/\char126 khonda
William H Kazez
Department of Mathematics
University of Georgia
GA 30602
http://www.math.uga.edu/\char126 will
Gordana Matić
Department of Mathematics
University of Georgia
GA 30602
http://www.math.uga.edu/\char126 gordana