Khovanov homology, its definitions and ramifications

Oleg Viro. "Khovanov homology, its definitions and ramifications." Fundamenta Mathematicae 184.1 (2004): 317-342. <http://eudml.org/doc/282696>.

@article{OlegViro2004,
abstract = {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.},
author = {Oleg Viro},
journal = {Fundamenta Mathematicae},
keywords = {Khovanov homology; links; Reidemeister moves},
language = {eng},
number = {1},
pages = {317-342},
title = {Khovanov homology, its definitions and ramifications},
url = {http://eudml.org/doc/282696},
volume = {184},
year = {2004},
}

TY - JOUR
AU - Oleg Viro
TI - Khovanov homology, its definitions and ramifications
JO - Fundamenta Mathematicae
PY - 2004
VL - 184
IS - 1
SP - 317
EP - 342
AB - 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.
LA - eng
KW - Khovanov homology; links; Reidemeister moves
UR - http://eudml.org/doc/282696
ER -