Double knot surgeries to S^4 and S^2 x S^2

Details Double knot surgeries to S^4 and S^2 x S^2 Double knot surgeries to S^4 and S^2 x S^2

2011-03-16

arxiv.org/abs/1103.3137v2

Mathematics

Geometric Topology

9 pages, 8 figures, final version to appear in International Journal of Mathematics

Scientific paper

It is known that S^4 is a union of two fishtails, and S^2 x S^2 is a union of
two cusps (glued along their boundaries). Here we prove that, for any choice of
knots K,L in S^3, performing knot surgery operations to S^4 and S^2 x S^2,
along both of the fishtails and cusps, respectively, do not change the
diffeomorphism type of these manifolds.

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