Topology Atlas | Conferences

Knots in Washington XXVII; 3rd Japan-USA Workshop in Knot Theory
January 9-11, 2009
George Washington University
Washington, DC, USA

Organizers
Yoshiyuki Ohyama (TWCU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Alexander Shumakovitch (GWU), Kouki Taniyama (Waseda and GWU), Tatsuya Tsukamoto (Osaka IT), Hao Wu (GWU), Akira Yasuhara (Tokyo GU)

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Presheaves, posets and Khovanov homology
by
Paul Turner
Fribourg/Heriot-Watt

I will outline some of the homology theory of presheaves of modules over posets and discuss how this is relevant to constructions in Khovanov homology. In particular I will discuss two applications of this point of view: (1) By fixing a number of crossings in a given link diagram one may build a cube of diagrams. I will explain how to construct a spectral sequence computing Khovanov homology for this situation; (2) It is known by the work of Przytycki that the Khovanov homology of a graph developed by Helme-Guizon-Rong, calculates Hochschild homology through a range of dimensions when the graph is the n-gon. I will explain how to extend this to define a homology theory for (possibly non-commutative) algebras starting with an arbitrary oriented graph.

Date received: November 14, 2008

Copyright © 2008 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # caxq-22.