Mathematical Sciences: Some Problems in Geometric Topology

Ferry将研究受控拓扑中的许多主题 和微分几何 这些问题大部分都与 问题是，“多少控制才足以使简单同伦 多面体之间的等价或多面体之间的同胚 拓扑流形“一个有趣的试验场， 受控理论处于拓扑学和 微分几何中的一些问题 显然在某种程度上受到控制，但没有 明显的控制空间。 费里已经解决了这样一个问题 在某种意义上，让问题自己控制 空间 他计划探索这些问题的进一步后果， 技术.

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.