Torsion of Khovanov homology

• Autorzy: Alexander N. Shumakovitch
• Języki publikacji: EN

Abstrakty

EN

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.

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: 343-364

Daty

wydano

2014

Twórcy

autor

Alexander N. Shumakovitch

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

Identyfikatory

DOI

10.4064/fm225-1-16