Mathematical Sciences: Homotopy Theory

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This research project involves work in several areas of algebraic topology. First of all, the principal investigator intends to continue his work with Stefan Jackowski and Bob Oliver on the homotopy theory of classifying spaces. Secondly, the principal investigator will attempt to apply the methods developed in that work to prove a stable version of Barratt's exponent conjecture. Finally, the principal investigator will continue his work with Ross Staffeldt on Topological Hochschild Homology and Waldhausen K-theory. To summarize, a variety of efforts will be pursued to explore, to perfect, and to apply sophisticated algebraic techniques in order better to understand and classify topological (i.e., a kind of geometric) structures.