Torsion of Khovanov homology
Tom 225 / 2014
Streszczenie
Khovanov homology is a recently introduced invariant of oriented links in $\mathbb R^3$. 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 $\mathbb Z_{2^k}$ factors in the canonical decomposition of the Khovanov homology groups for different values of $k$.
