Kauffman states, bordered algebras, and a bigraded knot invariant

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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.

Original languageEnglish (US)
Pages (from-to)1088-1198
Number of pages111
JournalAdvances in Mathematics
Volume328
DOIs
StatePublished - Apr 13 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Knot Floer homology
  • Knot invariants

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