Mathematical Sciences: Homotopy Theory and Its Applications

Ravenel教授希望继续他的研究，即复余边论在同伦理论中的应用。内森多费尔教授计划研究Moore空间的双圈空间的乘积分解，更广泛地说，研究单连通有限复形的双圈空间的乘积分解。他还计划研究某些函数空间的mod p同调的计算。这两项研究都是为了扩大高维流形分析和分类的一些标准代数技术的范围。流形本身是自然的几何对象，在理论物理和其他地方出现，通常是作为常方程或微分方程式的解集。

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.