Torsion in graph homology

• Autorzy: Laure Helme-Guizon , Józef H. Przytycki , Yongwu Rong
• Języki publikacji: EN

Abstrakty

EN

Khovanov homology for knots has generated a flurry of activity in the topology community. This paper studies the Khovanov type cohomology for graphs with a special attention to torsion. When the underlying algebra is ℤ[x]/(x²), we determine precisely those graphs whose cohomology contains torsion. For a large class of algebras, we show that torsion often occurs. Our investigation of torsion led to other related general results. Our computation could potentially be used to predict the Khovanov-Rozansky sl(m) homology of knots (in particular (2,n) torus knot). We also predict that our work is connected with Hochschild and Connes cyclic homology of algebras.

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 57M27: Invariants of knots and 3-manifolds
• 55N35: Other homology theories

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2006
• Tom: 190
• Numer: 1
• Strony: 139-177

Daty

wydano

2006

Twórcy

autor

Laure Helme-Guizon

• Department of Mathematics, The George Washington University, 1922 F street NW, Washington, DC 20052, U.S.A.

autor

Józef H. Przytycki

• Department of Mathematics, The George Washington University, Old Main Bldg, 1922 F St. NW, Washington, DC 20052, U.S.A.

autor

Yongwu Rong

• Department of Mathematics, The George Washington University, 1922 F street NW, Washington, DC 20052, U.S.A.

Identyfikatory

DOI

10.4064/fm190-0-5