A survey of 4-manifolds through the eyes of surgery

  title={A survey of 4-manifolds through the eyes of surgery},
  author={R. Kirby and L. Taylor},
  journal={arXiv: Geometric Topology},
Surgery theory is a method for constructing manifolds satisfying a given collection of homotopy conditions. It is usually combined with the s{cobordism theorem which constructs homeomorphisms or diieomorphisms between two similar looking manifolds. Building on work of Sullivan, Wall applied these two techniques to the problem of computing structure sets. While this is not the only use of surgery theory, it is the aspect on which we will concentrate in this survey. In dimension 4, there are two… Expand
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