Structure of knot and link concordance

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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.