Knot and braid invariants from contact homology II

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 2000

Primary: 57M27

Secondary: 53D35, 20F36

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

Lenhard Ng
Department of Mathematics Stanford University Stanford California 94305 USA
http://math.stanford.edu/~lng/
Siddhartha Gadgil
Stat-Math Unit Indian Statistical Institute Bangalore India

Volume 9, issue 3 (2005)

Lenhard Ng

Appendix: Siddhartha Gadgil

Abstract