Torsion in graph homology

Tom 190 / 2006

Laure Helme-Guizon, Józef H. Przytycki, Yongwu Rong Fundamenta Mathematicae 190 (2006), 139-177 MSC: Primary 57M27; Secondary 05C15, 55N35. DOI: 10.4064/fm190-0-5

Streszczenie

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 $\mathbb{Z}[x]/(x^2)$, 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.

Autorzy

  • Laure Helme-GuizonDepartment of Mathematics
    The George Washington University
    1922 F street NW
    Washington, DC 20052, U.S.A.
    e-mail
  • Józef H. PrzytyckiDepartment of Mathematics
    The George Washington University
    Old Main Bldg, 1922 F St. NW
    Washington, DC 20052, U.S.A.
    e-mail
  • Yongwu RongDepartment of Mathematics
    The George Washington University
    1922 F street NW
    Washington, DC 20052, U.S.A.
    e-mail

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