Remarks on definition of Khovanov homology

Abstract

Mikhail Khovanov in math.QA/9908171 defined, for a diagram of an oriented classical link, a collection of groups numerated by pairs of integers. These groups were constructed as homology groups of certain chain complexes. The Euler characteristics of these complexes are coefficients of the Jones polynomial of the link. The goal of this note is to rewrite this construction in terms more friendly to topologists. A version of Khovanov homology for framed links is introduced. For framed links whose Kauffman brackets are involved in a skein relation, these homology groups are related by an exact sequence.

11 pages, 4 figures

References in corpus (1)

• A functor-valued invariant of tangles

Cited by in corpus (11)

• Khovanov's homology for tangles and cobordisms
• Categorification of the Kauffman bracket skein module of I-bundles over surfaces
• An invariant of link cobordisms from Khovanov homology
• On the Khovanov and knot Floer homologies of quasi-alternating links
• Torsion of the Khovanov homology
• Homological thickness and stability of torus knots
• Khovanov homology and star-like isotopies
• Khovanov homology for signed divides
• A New Perspective for an Existing Homology Theory of Links Embedded in I-Bundles
• Homology of framed links embedded in thickened surfaces
• A Diagramless Link Homology