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.

arXiv comment45 pages, 26 figures. v4: Final version. Weak detection of trivial tangles upgraded to detection. Numerous expositional improvements. Comments welcome

References in corpus (15)

• Covariantly functorial wrapped Floer theory on Liouville sectors
• Knot and braid invariants from contact homology II, with an appendix written jointly with Siddhartha Gadgil
• Duality between Lagrangian and Legendrian invariants
• Knot and braid invariants from contact homology I
• A complete knot invariant from contact homology
• Sutures and contact homology I
• Liouville hypersurfaces and connect sum cobordisms
• Lifting pseudo-holomorphic polygons to the symplectisation of $P\times \mathbb{R}$ and applications
• Knot contact homology
• Symplectic and contact differential graded algebras
• Morse theory for manifolds with boundary
• A topological introduction to knot contact homology
• Fiber Floer cohomology and conormal stops
• Simplicial descent for Chekanov-Eliashberg dg-algebras
• Chekanov-Eliashberg dg-algebras for singular Legendrians

Cited by in corpus (1)

• Singular Legendrian unknot links and relative Ginzburg algebras