Mathematical Sciences: Homotopy Theory With An Emphasis On Maps Between Classifying Spaces

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The projected research involves work in four different areas of algebraic topology. First of all, the principal investigator intends to continue his investigation of maps between classifying spaces. Secondly, he intends to apply the methods developed in that subject to study the stable Barratt conjecture as formulated by Fred Cohen. Thirdly, he intends to extend and perhaps simplify recent work of Bokstedt on Hochschild homology and algebraic K-theory. Finally, he intends to investigate the relation between certain new primary operations in K-theory which he has constructed and the work of Kane and Lin on K-theory of finite H-spaces.