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Degenerate distributive homology is degenerate indeed
by
Krzysztof K. Putyra
Columbia University
Coauthors: Jozef H. Przytycki
The distributive homology of quandles and racks proved to be a useful tool in the theory of knots and links. After its discovery by Fenn, Rourke and Sanderson and then by Carter, Kamada and Saito, it was noticed that the distributive chain complex for a quandle splits into two parts, normalized and degenerate, immitating the simplicial homology theory. However, a degenerate complex is not acyclic, contrary to the simplicial theory. Recently, with Jozef Przytycki we managed to prove that the degenerate part, as its name suggests, is really degenerate: it is completely determined by the normalized homology.
In my talk I will describe the distributive chain complex associated to a quandle and, more generally, to a spindle, and how its splitting into degenerate and normalized parts. Then I will give a recursive formula for the degenerate part and sketch main ideas of its proof.
Date received: April 19, 2013
Copyright © 2013 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 # cbhe-05.