Volume 9, issue 1 (2005)

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
Knot and braid invariants from contact homology I

Lenhard Ng

Geometry & Topology 9 (2005) 247–297

arXiv: math.GT/0302099

Abstract

We introduce topological invariants of knots and braid conjugacy classes, in the form of differential graded algebras, and present an explicit combinatorial formulation for these invariants. The algebras conjecturally give the relative contact homology of certain Legendrian tori in five-dimensional contact manifolds. We present several computations and derive a relation between the knot invariant and the determinant.

Keywords
contact homology, knot invariant, braid representation, differential graded algebra
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 53D35, 20F36
References
Forward citations
Publication
Received: 16 July 2004
Accepted: 13 January 2005
Published: 26 January 2005
Proposed: Yasha Eliashberg
Seconded: Robion Kirby, Joan Birman
Authors
Lenhard Ng
Department of Mathematics
Stanford University
Stanford
California 94305
USA