Knot and braid invariants from contact homology I

Ng, Lenhard

doi:10.2140/gt.2005.9.247

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Knot and braid invariants from contact homology I

Lenhard Ng

Geometry & Topology 9 (2005) 247–297

DOI: 10.2140/gt.2005.9.247

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

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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

Volume 9, issue 1 (2005)