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

Primary: 57M27

Secondary: 20F36, 53D35

References

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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