Double knot surgeries to S4 and S2 x S2
Abstract
It is known that S4 is a union of two fishtails, and S2 x S2 is a union of two cusps (glued along their boundaries). Here we prove that, for any choice of knots K,L in S3, performing knot surgery operations to S4 and S2 x S2, along both of the fishtails and cusps, respectively, do not change the diffeomorphism type of these manifolds.
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