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Knot contact homology

dc.contributor.author Ekholm, T
dc.contributor.author Etnyre, JB
dc.contributor.author Ng, L
dc.contributor.author Sullivan, MG
dc.date.accessioned 2018-12-11T15:21:32Z
dc.date.available 2018-12-11T15:21:32Z
dc.date.issued 2013-04-30
dc.identifier.issn 1465-3060
dc.identifier.issn 1364-0380
dc.identifier.uri https://hdl.handle.net/10161/17788
dc.description.abstract The conormal lift of a link K in ℝ3is a Legendrian submanifold ∧Kin the unit cotangent bundle U*ℝ3of ℝ3with contact structure equal to the kernel of the Liouville form. Knot contact homology, a topological link invariant of K, is defined as the Legendrian homology of ∧K, the homology of a differential graded algebra generated by Reeb chords whose differential counts holomorphic disks in the symplectization R × U*ℝ3with Lagrangian boundary condition R × ∧K. We perform an explicit and complete computation of the Legendrian homology of ∧Kfor arbitrary links K in terms of a braid presentation of K, confirming a conjecture that this invariant agrees with a previously defined combinatorial version of knot contact homology. The computation uses a double degeneration: the braid degenerates toward a multiple cover of the unknot, which in turn degenerates to a point. Under the first degeneration, holomorphic disks converge to gradient flow trees with quantum corrections. The combined degenerations give rise to a new generalization of flow trees called multiscale flow trees. The theory of multiscale flow trees is the key tool in our computation and is already proving to be useful for other computations as well.
dc.language English
dc.publisher Mathematical Sciences Publishers
dc.relation.ispartof Geometry & Topology
dc.relation.isversionof 10.2140/gt.2013.17.975
dc.subject Science & Technology
dc.subject Physical Sciences
dc.subject Mathematics
dc.subject LEGENDRIAN SUBMANIFOLDS
dc.subject BRAID INVARIANTS
dc.subject SURGERY
dc.subject IMMERSIONS
dc.subject EMBEDDINGS
dc.subject R2N+1
dc.title Knot contact homology
dc.type Journal article
duke.contributor.id Ng, L|0407908
dc.date.updated 2018-12-11T15:21:31Z
pubs.begin-page 975
pubs.end-page 1112
pubs.issue 2
pubs.organisational-group Trinity College of Arts & Sciences
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.publication-status Published
pubs.volume 17


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