Volume 15, issue 1 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Braid ordering and the geometry of closed braid

Tetsuya Ito

Geometry & Topology 15 (2011) 473–498
Abstract

We study the relationships between the Dehornoy ordering of the braid groups and the topology and geometry of the closed braid complements. We show that the Dehornoy floor of braids, which is a nonnegative integer determined by the Dehornoy ordering, tells us the position of essential surfaces in the closed braid complements. Furthermore, we prove that if the Dehornoy floor of a braid is bigger than or equal to two, then the Nielsen–Thurston classification of braids and the geometric structure of the closed braid complements are in one-to-one correspondence.

Keywords
braid group, Dehornoy ordering, Nielsen–Thurston classification, geometric structure
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M50
References
Publication
Received: 30 September 2009
Revised: 14 December 2010
Accepted: 12 December 2010
Published: 25 March 2011
Proposed: Joan Birman
Seconded: David Gabai, Shigeyuki Morita
Authors
Tetsuya Ito
Graduate School of Mathematical Science
University of Tokyo
3-8-1 Komaba
Meguro-ku 153-8914
Japan
http://www.ms.u-tokyo.ac.jp/~tetitoh/