English

Remarks on Legendrian Self-Linking

Symplectic Geometry 2018-08-22 v2 High Energy Physics - Theory Geometric Topology

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.

Keywords

Cite

@article{arxiv.1503.06120,
  title  = {Remarks on Legendrian Self-Linking},
  author = {Chris Beasley and Brendan McLellan and Ruoran Zhang},
  journal= {arXiv preprint arXiv:1503.06120},
  year   = {2018}
}

Comments

42 pages, many figures; v2: minor revisions, published version

R2 v1 2026-06-22T08:58:09.364Z