Geometry & Topology 9 (2005) 1603–1637

DOI: 10.2140/gt.2005.9.1603

arXiv: math.GT/0303343

Abstract

We present a topological interpretation of knot and braid contact homology in degree zero, in terms of cords and skein relations. This interpretation allows us to extend the knot invariant to embedded graphs and higher-dimensional knots. We calculate the knot invariant for two-bridge knots and relate it to double branched covers for general knots. In the appendix we show that the cord ring is determined by the fundamental group and peripheral structure of a knot and give applications.

Keywords

contact homology, knot invariant, differential graded algebra, skein relation, character variety

Mathematical Subject Classification

Primary: 57M27

Secondary: 20F36, 53D35

References

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Publication

Received: 24 February 2005
Accepted: 16 August 2005
Published: 26 August 2005
Proposed: Yasha Eliashberg
Seconded: Robion Kirby, Ronald Fintushel

Authors