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A complete knot invariant from contact homology

Publication ,  Journal Article
Ekholm, T; Ng, L; Shende, V
Published in: Inventiones Mathematicae
March 1, 2018

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.

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Published In

Inventiones Mathematicae

DOI

ISSN

0020-9910

Publication Date

March 1, 2018

Volume

211

Issue

3

Start / End Page

1149 / 1200

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics
 

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Ekholm, T., Ng, L., & Shende, V. (2018). A complete knot invariant from contact homology. Inventiones Mathematicae, 211(3), 1149–1200. https://doi.org/10.1007/s00222-017-0761-1
Ekholm, T., L. Ng, and V. Shende. “A complete knot invariant from contact homology.” Inventiones Mathematicae 211, no. 3 (March 1, 2018): 1149–1200. https://doi.org/10.1007/s00222-017-0761-1.
Ekholm T, Ng L, Shende V. A complete knot invariant from contact homology. Inventiones Mathematicae. 2018 Mar 1;211(3):1149–200.
Ekholm, T., et al. “A complete knot invariant from contact homology.” Inventiones Mathematicae, vol. 211, no. 3, Mar. 2018, pp. 1149–200. Scopus, doi:10.1007/s00222-017-0761-1.
Ekholm T, Ng L, Shende V. A complete knot invariant from contact homology. Inventiones Mathematicae. 2018 Mar 1;211(3):1149–1200.
Journal cover image

Published In

Inventiones Mathematicae

DOI

ISSN

0020-9910

Publication Date

March 1, 2018

Volume

211

Issue

3

Start / End Page

1149 / 1200

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 0101 Pure Mathematics