Torsion of Khovanov homology

Alexander N. Shumakovitch. "Torsion of Khovanov homology." Fundamenta Mathematicae 225.0 (2014): 343-364. <http://eudml.org/doc/286418>.

@article{AlexanderN2014,
abstract = {Khovanov homology is a recently introduced invariant of oriented links in ℝ³. It categorifies the Jones polynomial in the sense that the (graded) Euler characteristic of Khovanov homology is a version of the Jones polynomial for links. In this paper we study torsion of Khovanov homology. Based on our calculations, we formulate several conjectures about the torsion and prove weaker versions of the first two of them. In particular, we prove that all non-split alternating links have their integer Khovanov homology almost determined by the Jones polynomial and signature. The only remaining indeterminacy is that one cannot distinguish between $ℤ_\{2^\{k\}\}$ factors in the canonical decomposition of the Khovanov homology groups for different values of k.},
author = {Alexander N. Shumakovitch},
journal = {Fundamenta Mathematicae},
keywords = {reduced Khovanov homology; torsion; homologically thin links; torsion simple links},
language = {eng},
number = {0},
pages = {343-364},
title = {Torsion of Khovanov homology},
url = {http://eudml.org/doc/286418},
volume = {225},
year = {2014},
}

TY - JOUR
AU - Alexander N. Shumakovitch
TI - Torsion of Khovanov homology
JO - Fundamenta Mathematicae
PY - 2014
VL - 225
IS - 0
SP - 343
EP - 364
AB - Khovanov homology is a recently introduced invariant of oriented links in ℝ³. It categorifies the Jones polynomial in the sense that the (graded) Euler characteristic of Khovanov homology is a version of the Jones polynomial for links. In this paper we study torsion of Khovanov homology. Based on our calculations, we formulate several conjectures about the torsion and prove weaker versions of the first two of them. In particular, we prove that all non-split alternating links have their integer Khovanov homology almost determined by the Jones polynomial and signature. The only remaining indeterminacy is that one cannot distinguish between $ℤ_{2^{k}}$ factors in the canonical decomposition of the Khovanov homology groups for different values of k.
LA - eng
KW - reduced Khovanov homology; torsion; homologically thin links; torsion simple links
UR - http://eudml.org/doc/286418
ER -