A complete knot invariant from contact homology

Journal Article (Journal Article)

We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to smooth isotopy. The enhancement consists of the (fully noncommutative) Legendrian contact homology associated to the union of the conormal torus of the knot and a disjoint cotangent fiber sphere, along with a product on a filtered part of this homology. As a corollary, we obtain a new, holomorphic-curve proof of a result of the third author that the Legendrian isotopy class of the conormal torus is a complete knot invariant.

Full Text

Duke Authors

Cited Authors

  • Ekholm, T; Ng, L; Shende, V

Published Date

  • March 1, 2018

Published In

Volume / Issue

  • 211 / 3

Start / End Page

  • 1149 - 1200

International Standard Serial Number (ISSN)

  • 0020-9910

Digital Object Identifier (DOI)

  • 10.1007/s00222-017-0761-1

Citation Source

  • Scopus