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Topology/Geometry Seminar
Thursday, February 1, 2007
5:30pm,
133 Hawthorn
David Blanc
University of Haifa
Generalized Quillen Cohomology.
Abstract: In the 1960's Quillen first formulated a general approach to homology and cohomology in algebraic settings, with cohomology functors represented by abelian group objects, and homology appearing as the derived functors of abelianization. However, if we try to apply this formula to topological spaces, we find the only abelian group objects are Eilenberg-Mac Lane spaces, which yield ordinary cohomology. Here we show how Quillen's approach may be extended to cover generalized cohomolgy theories, such as $K$-theory, cobordism (in various flavours), and so on, in a way that may help clarify the relationship between cohomology and homology.
The talk will not assume any special knowledge of homotopy theory or homotopical algebra.
We meet weekly on Thursday afternoons, with the third meeting of each month in Altoona. If you are interested in giving a talk in our seminar please contact one of the coordinators for the Spring 2006 semester: Aissa Wade and Wojciech Dorabiala.
