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A complete knot invariant from contact homology

dc.contributor.author Ekholm, T
dc.contributor.author Ng, L
dc.contributor.author Shende, V
dc.date.accessioned 2016-12-12T16:37:33Z
dc.identifier http://arxiv.org/abs/1606.07050v1
dc.identifier.uri https://hdl.handle.net/10161/13263
dc.description.abstract 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. Furthermore, we relate the holomorphic and sheaf approaches via calculations of partially wrapped Floer homology in the spirit of [BEE12].
dc.publisher Springer Science and Business Media LLC
dc.subject math.SG
dc.subject math.SG
dc.subject math.GT
dc.subject 53D42, 53D12, 55P50, 57R17, 57M27, 32S60
dc.title A complete knot invariant from contact homology
dc.type Journal article
duke.contributor.id Ng, L|0407908
pubs.author-url http://arxiv.org/abs/1606.07050v1
pubs.notes 56 pages
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Submitted


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