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Kauffman states, bordered algebras, and a bigraded knot invariant

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

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Abstract: We 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.
Publication Date: 13-Apr-2018
Electronic Publication Date: 22-Feb-2018
Citation: Ozsvath, Peter, Szabo, Zoltan. (2018). Kauffman states, bordered algebras, and a bigraded knot invariant. ADVANCES IN MATHEMATICS, 328 (1088 - 1198. doi:10.1016/j.aim.2018.02.017
DOI: doi:10.1016/j.aim.2018.02.017
ISSN: 0001-8708
EISSN: 1090-2082
Pages: 1088 - 1198
Type of Material: Journal Article
Journal/Proceeding Title: ADVANCES IN MATHEMATICS
Version: Author's manuscript

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