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Filtrations on the knot contact homology of transverse knots
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry. (Geometri)
2013 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 355, no 4, 1561-1591 p.Article in journal (Refereed) Published
Abstract [en]

We construct a new invariant of transverse links in the standard contactstructure on R^3. This invariant is a doubly filtered version of the knot contact homology differential graded algebra (DGA) of the link, see (Ekholm et al., Knot contacthomology, Arxiv:1109.1542, 2011; Ng, Duke Math J 141(2):365–406, 2008). Herethe knot contact homology of a link in R3is the Legendrian contact homology DGAof its conormal lift into the unit cotangent bundle SR^3of R^3, and the filtrations are constructed by counting intersections of the holomorphic disks of the DGA differential with two conormal lifts of the contact structure. We also present a combinatorial formula for the filtered DGA in terms of braid representatives of transverse links andapply it to show that the new invariant is independent of previously known invariantsof transverse links.

Place, publisher, year, edition, pages
Springer, 2013. Vol. 355, no 4, 1561-1591 p.
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URN: urn:nbn:se:uu:diva-197733DOI: 10.1007/s00208-012-0832-yISI: 000316870300012OAI: oai:DiVA.org:uu-197733DiVA: diva2:613969
Available from: 2013-04-02 Created: 2013-04-02 Last updated: 2013-05-07Bibliographically approved

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