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# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Fundamenta Mathematicae

### Tom 225 / 2014

Fundamenta Mathematicae 225 (2014), 277-303 MSC: 57M25, 57M27. DOI: 10.4064/fm225-1-13

#### Streszczenie

The goal of this paper is to address A. Shumakovitch's conjecture about the existence of ${\mathbb {Z}}_2$-torsion in Khovanov link homology. We analyze torsion in Khovanov homology of semi-adequate links via chromatic cohomology for graphs, which provides a link between link homology and the well-developed theory of Hochschild homology. In particular, we obtain explicit formulae for torsion and prove that Khovanov homology of semi-adequate links contains ${\mathbb {Z}}_2$-torsion if the corresponding Tait-type graph has a cycle of length at least $3$. Computations show that torsion of odd order exists but there is no general theory to support these observations. We conjecture that the existence of torsion is related to the braid index.

#### Autorzy

• Józef H. PrzytyckiDepartment of Mathematics
The George Washington University
Washington, DC 20052, U.S.A.
and
University of Gdańsk, Poland
and
University of Maryland
College Park, MD 20742, U.S.A.
e-mail