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

计划的研究工作涉及代数拓扑的四个不同领域。首先，首席研究员打算继续他在分类空间之间的地图研究。其次，他打算应用该学科发展的方法来研究由弗雷德·科恩提出的稳定巴拉特猜想。第三，他打算扩展和简化Bokstedt最近关于Hochschild同调和代数k理论的工作。最后，他打算研究他所构造的k理论中的一些新的初级运算与Kane和Lin关于有限h空间的k理论的工作之间的关系。

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.