Mathematical Sciences: Some Problems in Geometric Topology

首席研究员将致力于流形理论中的几个问题。他计划继续与S.Weinberger(芝加哥大学)一起研究拓扑刚性，并与他的同事Erik Peterson一起研究受控外科。他还对欧几里得空间的开子集的拓扑学刻画很感兴趣。在他指导下的一篇论文中，T·恩格尔女士将研究在拓扑刚性不成立的情况下的变形族。这些问题归根结底是探索我们生活的空间的基本结构，以及物理世界的其他抽象的基本结构。这些抽象有何不同，它们的共同点是什么？它们的基本性质在多大程度上遵循了一些基本的假设，而不存在任何变化的可能性？

The principal investigator will work on several problems in manifold theory. He plans to continue his work on topological rigidity with S. Weinberger (University of Chicago) and his work with his colleague Erik Peterson on controlled surgery. He is also interested in characterizing open subsets of Euclidean space topologically. In a thesis under his direction, Ms. T. Engel will study families of deformations in a situation where topological rigidity does not hold. These problems come down to probing the fundamental structure of the space in which we live and that of other abstractions of the physical world. How do these abstractions differ, and what is common to them all? To what extent do their basic properties follow from a few underlying assumptions without the possibility of any variation?