Topology Seminar

Title: Quillen cohomology of Pi-algebras
Speaker: Martin Frankland
Speaker Info: MIT
Brief Description:
Special Note:

A Pi-algebra is a graded group with additional structure that makes it look like the homotopy groups of a space. Given one such object A, one may ask if it can be realized topologically: Is there a space X such that pi_*(X) is isomorphic to A as a Pi-algebra, and if so, can we classify them?

Work of Blanc-Dwyer-Goerss provided an obstruction theory to realizing a Pi-algebra, where the obstructions (to existence and uniqueness) live in certain Quillen cohomology groups of Pi-algebras. What do these groups look like, and can we compute them?

We will tackle this question from the algebraic side, focusing on Quillen cohomology of truncated Pi-algebras. We will then use the obstruction theory to obtain results on the classification of certain 2-stage homotopy types, and compare them to what is known from other approaches.

Date: Monday, November 16, 2009
Time: 4:10pm
Where: Lunt 104
Contact Person: Prof. Paul Goerss
Contact email: pgoerss@math.northwestern.edu
Contact Phone: 847-491-8544
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