Mathematical Sciences: Homotopy Theory and Its Applications

Ravenel教授希望继续研究复协在同伦理论中的应用。Neisendorfer教授计划研究摩尔空间的双环空间的积分解，更一般地说，是单连通有限复合体的双环空间的积分解。他还计划研究某些函数空间的模p同调的计算。这两项研究都是为了扩展一些用于分析和分类高维流形的标准代数技术的范围。流形本身是自然的几何对象，出现在理论物理和其他领域，通常作为常方程或微分方程的解集。

Professor Ravenel wishes to continue his investigation of the applications of complex cobordism to homotopy theory. Professor Neisendorfer plans to study the product decompositions of double loop spaces of Moore spaces and, more generally, of the double loop spaces of simply connected finite complexes. He also plans to study the computation of the mod p homology of certain function spaces. Both investigations are efforts to expand the scope of some standard algebraic techniques for analyzing and classifying high- dimensional manifolds. Manifolds themselves are natural geometric objects which arise in theoretical physics and elsewhere, often as the solution sets of ordinary or differential equations.