The link surgery of $S^2\times S^2$ and Scharlemann's manifolds

Details The link surgery of $S^2\times S^2$ and Scharlemann's manifolds The link surgery of $S^2\times S^2$ and Scharlemann's manifolds

2010-11-24

arxiv.org/abs/1011.5308v3

Mathematics

Geometric Topology

20 pages, 30 figures

Scientific paper

Fintushel-Stern's knot surgery gave many pairs of exotic manifolds, which are homeomorphic but non-diffeomorphic. We show that if an elliptic fibration has two parallel, oppositely oriented vanishing circles (for example $S^2\times S^2$ or Matsumoto's $S^4$), then the knot surgery gives rise to standard manifolds. The diffeomorphism can give an alternative proof that Scharlemann's manifold is standard (originally by Akbulut [Ak1]).

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