Kauffman states, bordered algebras, and a bigraded knot invariant

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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 languageAmerican English
Pages (from-to)1088-1198
Number of pages111
JournalAdvances in Mathematics
StatePublished - Apr 13 2018

ASJC Scopus subject areas

  • General Mathematics


  • Knot Floer homology
  • Knot invariants


Dive into the research topics of 'Kauffman states, bordered algebras, and a bigraded knot invariant'. Together they form a unique fingerprint.

Cite this