Remarks on Legendrian Self-Linking
arXiv:1503.06120 · doi:10.1063/1.5006069
Abstract
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 Euclidean space. Our definition is based upon a 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.
42 pages, many figures; v2: minor revisions, published version