Torsion in Khovanov homology of semi-adequate links

• Autorzy: Józef H. Przytycki , Radmila Sazdanović
• Języki publikacji: EN

Abstrakty

EN

The goal of this paper is to address A. Shumakovitch's conjecture about the existence of ℤ₂-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 ℤ₂-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.

Kategorie tematyczne

• 57M27: Invariants of knots and 3-manifolds
• 57M25: Knots and links in S 3

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2014
• Tom: 225
• Numer: 1
• Strony: 277-303

Daty

wydano

2014

Twórcy

autor

Józef H. Przytycki

• Department of Mathematics, The George Washington University, Washington, DC 20052, U.S.A.
• University of Gdańsk, Poland
• University of Maryland, College Park, MD 20742, U.S.A.

autor

Radmila Sazdanović

• Department of Mathematics, North Carolina State University, Raleigh, NC 27695, U.S.A.

Identyfikatory

DOI

10.4064/fm225-1-13