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Organizers |
Simplicial approach to distributive homology
by
Krzysztof Putyra
Columbia University
Coauthors: Jozef H. Przytycki,
Alissa Crans
Most algebraic homology theories are reflected by topological constructions: group homology H(G) is given by homology of the Eilenberg-MacLane space K(G, 1), two-term rack homology HR(X) is given by the space BX defined by Fenn and Rourke, examined later also by Clauwens and Eisermann. In my talk I will construct a space EX for any shelf X, which gives one-term distributive homology of X. The construction is very similar to EG for groups. The idea was already mentioned by Sikora, but he never used it for actual computation. During my talk I will recover from EX a few known already results about distributive homology of certain racks and strengthen others. One suprising result is existence of torsion, which I will try to explain.
I will start my talk with recalling briefly definitions of distributive operations and distributive homology. Then I will talk about simplicial sets, focusing on its connection to topology of CW-complexes. In this setting I will show how EG is constructed for a group and explain, why a similar construction should hold for racks and shelves in general. In the last 15min I will recover and strengthen a few results using this simplicial set and speculate about conjectured exponential growth of distributive homology.
Date received: March 12, 2012
Copyright © 2012 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 # cbek-17.