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Organizers |
Mirror knots have dual odd Khovanov homology
by
Krzysztof Putyra
Columbia University
Coauthors: Wojciech Lubawski
Polish Academy of Sciences
An odd Khovanov homology is a modification of sl_2 link homology defined in 2008 by P. Ozsvath and Z. Szabo. Instead of a symmetric algebra they used an antisymmetric one and got a different link homology theory that categorifies the Jones polynomial. One year later I generalized both constructions to a theory with three parameters. Together with W. Lubawski we were able to find two gradings in the cube of resolutions, each splitting the cube into isomorphic pieces. This can be used to eliminate two parameters. Hence, up to isomorphism only two theories exist. As a consequence, mirror knots have dual chain complexes in both cases.
Date received: April 28, 2011
Copyright © 2011 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 # cbcc-21.