DOUBLE KNOT SURGERIES TO S4 AND S2 × S2

Abstract

It is known that S4 is a union of two fishtails, and S2 × S2 is a union of two cusps (glued along their boundaries). Here we prove that for any choice of knots K, L ⊂ S3 the knot surgery operations [Formula: see text] and S2 × S2 ⇝ (S2 × S2)K, L along both of these fishtails and cusps, respectively, do not change the diffeomorphism type of these manifolds.