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Odd homology of tangles and cobordisms
by
Krzysztof Putyra
Jagiellonian University
On the previous conference I introduced cobordisms with chronology, a special projection on the unit interval [0, 1], and used them to build a chain complex for a given link diagram, similar to the one of Bar-Natan. The complex is a link invariant unpo chain-homotopies and slightly modified S/T/4Tu relations. Then, using an appropriate functor into the category of modules one can obtain computable invariants. I will show that for modules over an integral domain, only two theories can be obtained in this way: Khovanov's and the odd one.
Another think is to define the chain complex for tangles, using cobordisms with corners. After a small refinement of this category, one can extend the construction to tangle cobordisms as well. This can lead us to invariants of knotted surfaces, however defined only upto sign.
Date received: December 17, 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-59.