Chain homotopy maps for Khovanov homology

Noboru Ito*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Explicit chain homotopy maps and chain maps for the Reidemeister moves of Khovanov homology are often useful for several proofs of the isotopy invariance of Khovanov homology. However, such maps are missing except for the first Reidemeister moves given by Viro. In this paper, such chain homotopy maps and chain maps are obtained explicitly for the second and third Reidemeister moves (Sec. 2). Some applications are given to show the usefulness of these maps (Sec. 3).

Original languageEnglish
Pages (from-to)127-139
Number of pages13
JournalJournal of Knot Theory and its Ramifications
Issue number1
Publication statusPublished - 2011 Jan


  • chain homotopy maps
  • Khovanov homology

ASJC Scopus subject areas

  • Algebra and Number Theory


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