Knot and braid invariants from contact homology II, 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.

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper36.abs.html

References in corpus (5)

• Functors and Computations in Floer homology with Applications Part II
• Floer homology and the heat flow
• Knot and braid invariants from contact homology II, with an appendix written jointly with Siddhartha Gadgil
• Knot and braid invariants from contact homology I
• The nonuniqueness of Chekanov polynomials of Legendrian knots

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