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Topology/Geometry Seminar
Thursday, March 24, 2005
5:10-6:10pm,
122 Pond Lab (UP)
Mark Johnson
Penn State Altoona
Realizing Diagrams of π-algebras
Abstract: The category of Pi-algebras is the category of universal algebras most closely approximating the graded homotopy groups of a connected topological space. Thus, a Pi-algebra consists of a positively graded group equipped with certain algebraic operations, like Whitehead products. The most important question yet addressed about a Pi-algebra is trying to find a realization, that is, a space X so that the graded homotopy groups of X are the given Pi-algebra. A complete obstruction theory answering this question has been given by Blanc-Dwyer-Goerss, based on earlier work by Dwyer-Kan-Stover. I will describe an obstruction theory for realizing a given diagram of Pi-algebras, such as a short exact sequence, from joint work with David Blanc and James Turner. This fits under the general heading of rigidifying homotopy commutative diagrams, hence our obstructions are related to Toda brackets in certain cases.
