Journal of Mathematical Physics
The Thurston-Bennequin invariant provides one notion of self-linking for any homologically-trivial Legendrian curve in a contact three-manifold. Here we discuss related analytic notions of self-linking for Legendrian knots in R3. Our definition is based upon reformulation of the elementary Gauss linking integral and is motivated by ideas from supersymmetric gauge theory. We recover the Thurston-Bennequin invariant as a special case.
Journal of Mathematical Physics 59, 083503 (2018); doi: 10.1063/1.5006069
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