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CHAIN HOMOTOPY MAPS FOR KHOVANOV HOMOLOGY

NOBORU ITO

Department of Mathematics, Waseda University, 169-8555 Tokyo, Japan

https://doi.org/10.1142/S0218216511008656Cited by:3 (Source: Crossref)

Abstract

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).

Keywords:

AMSC: 57M25, 57M27

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