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Topology/Geometry Seminar
Thursday, March 17, 2005
5:30-7:00pm,
146 Hawthorn (Altoona)
Mark Johnson
Penn State Altoona
Resolution Model Categories
Abstract: Given a model category C, one would like to have a model structure on the category of simplicial objects of C. Actually, there are many such structures in general, so one sets out trying to choose among them. I will review the relevant details of one such choice, called a resolution model structure, which is well-behaved in terms of the two different types of homotopy groups for a simplicial object in C. If time allows, I will also discuss the spiral exact sequence relating these two types of homotopy groups and an additional structure called an E_2 model category structure. The primary purpose is to give a complete discussion of the technical background for the next talk, which will depend upon the existence of these constructions for C a category of diagrams of topological spaces.
