Double knot surgeries to S⁴ and S² x S²

الأصل · EN

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.