Mathematical Sciences: Geometric Questions in Algebraic Topology

曼恩教授将调查两个独立的项目， 代数拓扑 这些项目研究的模空间 瞬子与分段线性群作用 流形和带边模 第一个项目，代表与教授的联合工作 C.P.博耶，继续教授博耶正在进行的计划， Mann研究瞬子模空间的几何， 出现在微分几何公式杨米尔斯 规范理论，通过使用迭代回路空间的理论， 它们的相关同源操作。 第二个项目，代表与教授的联合工作 E.Y.米勒，是基于在很大程度上的工作教授 Mann和米勒关于等变函数空间，分类 等变分段线性结构空间及相关 行动地图 这项工作将使曼教授能够回答 几何问题，虽然众所周知的光滑流形， 对于分段线性流形是未知的。 发现理论物理和拓扑学是令人欣慰的 像第一个项目一样互相激励。

Professor Mann will investigate two independent projects in algebraic topology. These projects study moduli spaces of instantons and piecewise linear group actions on piecewise linear manifolds and bordism modules. The first project, representing joint work with Professor C.P. Boyer, continues the ongoing program of Professors Boyer and Mann to study the geometry of moduli spaces of instantons, which arise in the differential geometric formulation of Yang-Mills gauge theory, by using the theory of iterated loop spaces and their associated homology operations. The second project, representing joint work with Professor E.Y. Miller, is based in large part on the work of Professors Mann and Miller on equivariant function spaces, classifying spaces for equivariant piecewise linear structures and associated action maps. This work will allow Professor Mann to answer geometric questions which, while well-known for smooth manifolds, are now unknown for piecewise linear manifolds. It is gratifying to find theoretical physics and topology stimulating each other as in the first project.