Knot and braid invariants from contact homology I

Details Knot and braid invariants from contact homology I Knot and braid invariants from contact homology I

2003-02-10

arxiv.org/abs/math/0302099v4

Geom. Topol. 9(2005) 247-297

Mathematics

Geometric Topology

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper8.abs.html

Scientific paper

We introduce topological invariants of knots and braid conjugacy classes, in the form of differential graded algebras, and present an explicit combinatorial formulation for these invariants. The algebras conjecturally give the relative contact homology of certain Legendrian tori in five-dimensional contact manifolds. We present several computations and derive a relation between the knot invariant and the determinant.

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