#### Volume 14, issue 5 (2014)

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Operations on open book foliations

### Tetsuya Ito and Keiko Kawamuro

Algebraic & Geometric Topology 14 (2014) 2983–3020
##### Abstract

We study $b$–arc foliation changes and exchange moves 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: we show that 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.

##### Keywords
open book foliation, exchange move, bypass move, stabilization
Primary: 57M27