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University Park
Altoona

Thursday, December 9, 2004
5:30-7:00pm, 209 Holt (Altoona)

Bernard Badzioch
SUNY Buffalo

Categorical algebra of mapping spaces

Abstract: One of the successes of homotopy theory was a description of the structure of n-fold loop spaces,that is spaces of maps from an $n$-dimensional sphere $S^n$ to a given space $X$. A remarkable feature of this description is that one can decide if a space $Y$ if a homotopy type of an $n$-fold loop space just by looking at a certain algebraic structure on $Y$. The talk will give an overview of these results. It will also explain how the algebraic formalism involved can be extended to mapping spaces other than loop spaces and why - at least in some cases - algebraic structure is not enough to describe the structure of the mapping spaces. This work is a joint project with W. Dorabiala.

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