Operations on open book foliations

Abstract

We study b-arc foliation change and exchange move of open book foliations which generalize the corresponding operations in braid foliation theory. We also define a bypass move as an analogue of Honda's bypass attachment operation. As applications, we study how open book foliations change under a stabilization of the open book. We also generalize Birman-Menasco's split/composite braid theorem: Closed braid representatives of a split (resp. composite) link in a certain open book can be converted to a split (resp. composite) closed braid by applying exchange moves finitely many times.

32 pages, 32 figures

References in corpus (3)

• Right-veering diffeomorphisms of compact surfaces with boundary II
• Lectures on open book decompositions and contact structures
• Visualizing overtwisted discs in open books

Cited by in corpus (6)

• Foliated Open Books
• Quasi right-veering braids and non-loose links
• Overtwisted discs in planar open books
• Visualizing overtwisted discs in open books
• The defect of Bennequin-Eliashberg inequality and Bennequin surfaces
• On a relation between the self-linking number and the braid index of closed braids in open books