Structure of knot and link concordance

低维拓扑学是一门迷人的学科，它与理解三维和四维空间有关，就像我们居住的宇宙一样。 我调查的拓扑结构的3-和4维流形，特别是结和链接和谐。 本文研究了圆在三维空间中的嵌入和曲面在四维空间中的嵌入。 我的建议旨在更好地理解和谐空间的结构。纽结与链环协调是四维流形中曲面嵌入问题的关键局部问题，也是四维流形分类的核心。我主要使用代数和几何工具，但有时也使用分析方法来解决问题。

Low dimensional topology is a fascinating subject, concerned with understanding spaces of dimension 3 and 4, much like the universe we inhabit.  I investigate the topology of 3- and 4-dimensional manifolds, in particular knot and link concordance.  This is the study of embeddings of circles in 3-space and embeddings of surfaces in 4-space.  My proposal aims to achieve a greater understanding of the structure of concordance spaces. Knot and link concordance is the key local question in the problem of embedding surfaces in 4-manifolds, which is central to attempts to classify 4-dimensional manifolds. I use principally algebraic and geometric tools, but sometimes analytic methods as well, to attack the questions.