Knot and braid invariants from contact homology II, with an appendix written jointly with Siddhartha Gadgil

Details Knot and braid invariants from contact homology II, with an appendix written jointly with Siddhartha Gadgil Knot and braid invariants from contact homology II, with an appendix written jointly with Siddhartha Gadgil

2003-03-27

arxiv.org/abs/math/0303343v3

Geom. Topol. 9(2005) 1603-1637

Mathematics

Geometric Topology

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

Scientific paper

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.

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