Volume 7, issue 3 (2007)

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

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A homological definition of the HOMFLY polynomial

Stephen Bigelow

Algebraic & Geometric Topology 7 (2007) 1409–1440

arXiv: arXiv:math/0608527

Abstract

We give a new definition of the knot invariant associated to the Lie algebra suN+1. Knowing these for all N is equivalent to knowing the HOMFLY polynomial. Our definition requires that the knot or link be presented as the plat closure of a braid. The invariant is then a homological intersection pairing between two immersed manifolds in a configuration space of points in a disk. This generalizes previous work on the Jones polynomial, which is the case N = 1.

Keywords
HOMFLY polynomial, braid group, plat closure, bridge position, configuration space
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27, 20F36
References
Publication
Received: 23 August 2006
Revised: 14 September 2007
Accepted: 14 September 2007
Published: 15 October 2007
Authors
Stephen Bigelow
Department of Mathematics
University of California at Santa Barbara
California 93106
USA
http://www.math.ucsb.edu/~bigelow/