Mathematical Sciences: Topology and Geometry of Manifolds

科克伦博士计划继续他的研究一致性， 链接和不变量的流形的尺寸3和4。 的 科克伦博士正在研究的关联现象表明， 与四维分类有关的现象 空间. 他还将研究方面的流形， 在物理学中的意义。 三维和四维流形对我们很重要， 因为我们生活在一个三维流形中， 时间维度和四维流形如果我们不这样做。 这项工作的有趣之处在于， 物理学解决的是纯粹的几何问题，而不仅仅是其他问题。 这是一个更值得期待的地方。

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.