Volume 9, issue 3 (2005)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Knot and braid invariants from contact homology II

Lenhard Ng

Appendix: Siddhartha Gadgil

Geometry & Topology 9 (2005) 1603–1637

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 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