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A 2-category of dotted cobordisms and a universal odd link homology
by
Krzysztof Putyra
Columbia University
There are two kinds of Khovanov-type link homology theories: even introduced by M.Khovanov in 1999 and odd constructed by P.Ozsvath, Z.Szabo and J.Rasmussen in 2007. Both are derived from the cube of resolutions of a link diagram. However, the odd version is not given by a Frobenius algebra but only by a projective functor. In 2008, I rewrote the construction using chronological cobordisms, i.e. cobordisms equipped with special projections onto a unit interval (in fact it is a 2-category). On a side, I obtained a homology theory that specializes to both even and odd link homologies. Recently, I have found also a chronological version of dotted cobordisms and the neck-cutting relation, what simplifies the whole construction and gives in some sense a universal theory. Some implications are:
- non-existence of odd vesion of Lie theory
- there is only one dot in the odd theory over a field
Paper reference: arXiv:1004.0889
Date received: April 28, 2010
Copyright © 2010 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 # cbaf-12.