3‐manifolds efficiently bound 4‐manifolds

  title={3‐manifolds efficiently bound 4‐manifolds},
  author={F. Costantino and D. Thurston},
  journal={Journal of Topology},
  • F. Costantino, D. Thurston
  • Published 2008
  • Mathematics
  • Journal of Topology
  • It has been known since 1954 that every 3-manifold bounds a 4-manifold. Thus, for instance, every 3-manifold has a surgery diagram. There are several proofs of this fact, but little attention has been paid to the complexity of the 4-manifold produced. Given a 3-manifold M 3 of complexity n, we construct a 4-manifold bounded by M of complexity , where the ‘complexity’ of a piecewise-linear manifold is the minimum number of n-simplices in a triangulation.The proof goes through the notion of… CONTINUE READING
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