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A complete knot invariant from contact homology
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. Inst Mittag Leffler, S-18260 Djursholm, Sweden..
Duke Univ, Dept Math, Durham, NC 27708 USA..
Univ Calif Berkeley, Dept Math, 970 Evans Hall, Berkeley, CA 94720 USA..
2018 (English)In: Inventiones Mathematicae, ISSN 0020-9910, E-ISSN 1432-1297, Vol. 211, no 3, p. 1149-1200Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
SPRINGER HEIDELBERG , 2018. Vol. 211, no 3, p. 1149-1200
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-347548DOI: 10.1007/s00222-017-0761-1ISI: 000424998500005OAI: oai:DiVA.org:uu-347548DiVA, id: diva2:1194957
Funder
Knut and Alice Wallenberg FoundationSwedish Research CouncilAvailable from: 2018-04-04 Created: 2018-04-04 Last updated: 2018-04-04Bibliographically approved

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Ekholm, Tobias

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