Volume 14, issue 5 (2014)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
Mathematical Subject Classification 2010
Primary: 57M27
References
Publication
Received: 15 October 2013
Revised: 15 January 2014
Accepted: 28 January 2014
Published: 5 November 2014
Authors
Tetsuya Ito
Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502
Japan
http://www.kurims.kyoto-u.ac.jp/~tetitoh/
Keiko Kawamuro
Department of Mathematics
The University of Iowa
Iowa City, IA 52242-1419
USA