Mathematical Sciences: Topology and Geometry of Manifolds

科克伦博士计划继续他关于环的一致性以及3维和4维流形的不变量的研究。科克伦博士正在研究的链接现象预示着与四维空间分类有关的新现象。他还将研究在物理学背景下具有重要意义的流形的各个方面。三维和四维流形对我们很重要，因为如果我们忽略时间维度，我们就生活在三维流形中，如果我们不这样做，我们就生活在四维流形中。其中一些工作的有趣之处在于，来自物理学的想法正在解决纯粹的几何问题，而不仅仅是反过来，这更是意料之中的。

Dr. Cochran plans to continue his studies on concordance of links and on invariants of manifolds of dimensions 3 and 4. The linking phenomena Dr. Cochran is studying are indicative of new phenomena relating to the classification of four-dimensional spaces. He will also study aspects of manifolds which have significance in the context of physics. Three and four-dimensional manifolds are important to us, since we live in a three-dimensional manifold if we ignore the time dimension and a four-dimensional manifold if we do not. What is intriguing about some of this work is that ideas from physics are solving purely geometric problems, not only the other way around, which is more to be expected.