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Kauffman states, bordered algebras, and a bigraded knot invariant

Author(s): Ozsvath, Peter Steven; Szabo, Zoltan

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dc.contributor.authorOzsvath, Peter Steven-
dc.contributor.authorSzabo, Zoltan-
dc.identifier.citationOzsvath, Peter, Szabo, Zoltan. (2018). Kauffman states, bordered algebras, and a bigraded knot invariant. ADVANCES IN MATHEMATICS, 328 (1088 - 1198. doi:10.1016/j.aim.2018.02.017en_US
dc.description.abstractWe define and study a bigraded knot invariant whose Euler characteristic is the Alexander polynomial, closely connected to knot Floer homology. The invariant is the homology of a chain complex whose generators correspond to Kauffman states for a knot diagram. The definition uses decompositions of knot diagrams: to a collection of points on the line, we associate a differential graded algebra; to a partial knot diagram, we associate modules over the algebra. The knot invariant is obtained from these modules by an appropriate tensor product.en_US
dc.format.extent1088 - 1198en_US
dc.relation.ispartofADVANCES IN MATHEMATICSen_US
dc.rightsAuthor's manuscripten_US
dc.titleKauffman states, bordered algebras, and a bigraded knot invarianten_US
dc.typeJournal Articleen_US

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