Khovanov homology, its definitions and ramifications

• Autorzy: Oleg Viro
• Języki publikacji: EN

Abstrakty

EN

Mikhail Khovanov defined, for a diagram of an oriented classical link, a collection of groups labelled by pairs of integers. These groups were constructed as the homology groups of certain chain complexes. The Euler characteristics of these complexes are the coefficients of the Jones polynomial of the link. The original construction is overloaded with algebraic details. Most of the specialists use adaptations of it stripped off the details. The goal of this paper is to overview these adaptations and show how to switch between them. We also discuss a version of Khovanov homology for framed links and suggest a new grading for it.

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds
• 57M25: Knots and links in S 3

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 184
• Numer: 1
• Strony: 317-342

Daty

wydano

2004

Twórcy

autor

Oleg Viro

• Department of Mathematics, Uppsala University, Box 480, S-751 06 Uppsala, Sweden

Identyfikatory

DOI

10.4064/fm184-0-18