Tangle contact homology

Abstract

Knot contact homology is an ambient isotopy invariant of knots and links in ${\mathbb{R}}^3$. The purpose of this paper is to extend this definition to an ambient isotopy invariant of tangles and prove that gluing of tangles gives a gluing formula for knot contact homology. As a consequence of the gluing formula we obtain that the tangle contact homology detects triviality of tangles.

45 pages, 26 figures. v4: Final version. Weak detection of trivial tangles upgraded to detection. Numerous expositional improvements. Comments welcome

References in corpus (1)

• Simplicial descent for Chekanov-Eliashberg dg-algebras

Cited by in corpus (1)

• Singular Legendrian unknot links and relative Ginzburg algebras