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Torsion in H^2, v(G)-2_A_2(G) and its applications to Khovanov homology of adequate diagrams.
by
Jozef H. Przytycki
George Washington University
Coauthors: Radmila Sazdanovic (GWU)
It has been conjectured by Alexander Shumakovitch (announced at Knots in Poland conference in 2003) that any link which is not a connected or disjoint sum of Hopf links and trivial links has a torsion in Khovanov homology. Shumakovitch demonstrated the conjecture for alternating links and Marta Asaeda and myself generalized it for a large class of adequate links (including strongly adequate links). Here we prove the conjecture for those + adequate links D, whose + adequate diagram D has an associated s+ state graph Gs+(D) with a cycle of length at least 3. In our work we approximate Khovanov homology of D by chromatic (Helme-Guizon-Rong) cohomology of Gs+(D). In particular, we prove that for a connected simple graph G of v vertices and cyclomatic number p1 tor H2, v(G)-2(G) is equal to Z2p1 for G bipartite and Z2p1-1 otherwise.
Date received: December 6, 2007
Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavo-17.