Geometry & Topology, Vol. 9 (2005) Paper no. 36, pages 1603--1637.

Knot and braid invariants from contact homology II

Lenhard Ng
with an appendix written jointly with Siddhartha Gadgil

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

AMS subject classification. Primary: 57M27. Secondary: 53D35, 20F36.

E-print: arXiv:math.GT/0303343

DOI: 10.2140/gt.2005.9.1603

Submitted to GT on 24 February 2005. Paper accepted 16 August 2005. Paper published 26 August 2005.

Notes on file formats

Lenhard Ng
LN: Department of Mathematics, Stanford University
Stanford, CA 94305, USA
SG: Stat-Math Unit, Indian Statistical Institute
Bangalore, India

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