Tangle contact homology
Abstract
Knot contact homology is an ambient isotopy invariant of knots and links in R3. 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.
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