Mathematical Sciences: Algebraic and Differential Topology

科克伦博士计划继续研究链环的一致性以及三维和四维流形的不变量。他正在寻找的链接现象将预示着与四维空间分类有关的新现象。他将研究三维和四维流形的不变量，这些流形具有微分几何解释，并在物理背景下具有重要意义。

Dr. Cochran plans to continue his studies on concordance of links and on invariants of manifolds of dimensions three and four. The linking phenomena he is seeking would be indicative of new phenomena relating to the classification of four-dimensional spaces. He will study invariants of three and four-dimensional manifolds which have a differential-geometric interpretation and have significance in the context of physics.