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Embedded annuli and Jones' conjecture

Douglas J LaFountain and William W Menasco
Algebraic & Geometric Topology 14 (2014) 3589–3601
DOI: 10.2140/agt.2014.14.3589
Abstract

We show that after stabilizations of opposite parity and braid isotopy, any two braids in the same topological link type cobound embedded annuli. We use this to prove the generalized Jones’ conjecture relating the braid index and algebraic length of closed braids within a link type, following a reformulation of the problem by Kawamuro.

Keywords
links, braids, braid foliations
Mathematical Subject Classification 2010
Primary: 57M25
Secondary: 57R17, 20F36
References
Publication
Received: 17 October 2013
Revised: 2 January 2014
Accepted: 27 April 2014
Published: 15 January 2015
Authors
Douglas J LaFountain
Department of Mathematics
Western Illinois University
Macomb, IL 61455
USA
http://www.wiu.edu/users/dl127/
William W Menasco
Department of Mathematics
University at Buffalo
Buffalo, NY 14260
USA
http://www.math.buffalo.edu/~menasco/