Torsion of Khovanov homology

Volume 225 / 2014

Alexander N. Shumakovitch Fundamenta Mathematicae 225 (2014), 343-364 MSC: 57M25, 57M27. DOI: 10.4064/fm225-1-16


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 $k$.


  • Alexander N. ShumakovitchDepartment of Mathematics
    The George Washington University
    Monroe Hall
    2115 G St. NW
    Washington, DC 20052, U.S.A.

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