Special Issue — Devoted to the 60th birthday of J. H. Przytycki; Guest Editors: M. K. Dabkowski, V. Harizanov, L. H. Kauffman, J. H. Przytycki, R. Sazdanovic and A. SikoraNo Access

Patterns in Khovanov link and chromatic graph homology

Radmila Sazdanovic

Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA

E-mail Address: rsazdanovic@math.ncsu.edu

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and

Daniel Scofield

Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA

E-mail Address: dscofie@ncsu.edu

Corresponding author.

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https://doi.org/10.1142/S0218216518400072Cited by:4 (Source: Crossref)

Abstract

Khovanov homology of a link and chromatic graph homology are known to be isomorphic in a range of homological gradings that depend on the girth of a graph. We discuss patterns shared by these two homology theories. In particular, we improve the bounds for the homological span of chromatic homology by Helme–Guizon, Przytycki and Rong. An explicit formula for the rank of the third chromatic homology group on the main diagonal is given and used to compute the corresponding Khovanov homology group and the fourth coefficient of the Jones polynomial for links with certain diagrams.

Keywords:

AMSC: 57M25, 57M27

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