Mathematical Sciences: Some Problems in Geometric Topology

费里将研究控制拓扑和微分几何中的许多主题。这些问题中的大多数都涉及到这样一个问题：“多少控制足以强制多面体之间的简单同胚等价或拓扑流形之间的同胚等价？”控制理论的一个有趣的试验场是在拓扑学和微分几何的交界处，那里有一些问题在某种程度上显然是可控的，但没有明显的控制空间。Ferry已经解决了一个这样的问题，在某种意义上，让问题构建自己的控制空间。他计划进一步探索这些技术的影响。

Ferry will study a number of topics in controlled topology and differential geometry. Most of these problems bear on the problem, "How much control is enough to force simple homotopy equivalence between polyhedra or homeomorphism between topological manifolds?" An interesting testing ground for controlled theories is on the borderline between topology and differential geometry, where there are problems which are obviously controlled in some way but for which there is no obvious control space. Ferry has already solved one such problem by, in some sense, letting the problem construct its own control space. He plans to explore further ramifications of these techniques.