Open Book Foliations

Abstract

We study open book foliations on surfaces in 3-manifolds, and give applications to contact geometry of dimension 3. We prove a braid-theoretic formula of the self-linking number of transverse links, which reveals an unexpected link to the Johnson-Morita homomorphism in mapping class group theory. We also give an alternative combinatorial proof to the Bennequin-Eliashberg inequality.

47 pages, 34 figures, accepted by Geometry and Topology. Title, abstract, expositions have been changed. The last section of Version 1 is now included in another paper "Visualizing overtwisted discs in open books" (arXiv:1310.6404)

References in corpus (4)

• Stabilization in the braid groups II: Transversal simplicity of knots
• Stabilization in the braid groups I: MTWS
• The Self-Linking Number in Annulus and Pants Open Book Decompositions
• Braiding Knots in Contact 3-Manifolds

Cited by in corpus (8)

• Operations on open book foliations
• Quasipositive links and Stein surfaces
• Non-looseness of non-loose knots
• Rectangular diagrams of surfaces: representability
• Foliated Open Books
• A User's Guide to Morse Foliated Open Books
• A friendly introduction to the bordered contact invariant
• On a relation between the self-linking number and the braid index of closed braids in open books