Mathematical Sciences: Homotopy Theory

该研究项目涉及以下几个领域的工作： 代数拓扑 首先，首席研究员 他打算继续与斯特凡·杰克沃斯基和鲍勃·奥利弗合作 关于空间分类的同伦理论 二是 主要研究者将尝试应用这些方法 在那项工作中发展起来的，以证明巴拉特的稳定版本 指数猜想 最后，首席研究员将 继续他的工作与罗斯Staffeldt拓扑Hochschild 同调与Waldhausen K理论 总之，将作出各种努力， 探索，完善，并应用复杂的代数 技术，以便更好地理解和分类拓扑 (i.e.,一种几何）结构。

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.