Operations on open book foliations

Ito, Tetsuya; Kawamuro, Keiko

doi:10.2140/agt.2014.14.2983

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Operations on open book foliations

Tetsuya Ito and Keiko Kawamuro

Algebraic & Geometric Topology 14 (2014) 2983–3020

DOI: 10.2140/agt.2014.14.2983

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

Volume 14, issue 5 (2014)