Pochette surgery of 4-sphere

Abstract

Iwase and Matsumoto defined `pochette surgery' as a cut-and-paste on 4-manifolds along a 4-manifold homotopy equivalent to $S^2\vee S^1$. The first author in [10] studied infinitely many homotopy 4-spheres obtained by pochette surgery. In this paper we compute the homology of pochette surgery of any homology 4-sphere by using `linking number' of a pochette embedding. We prove that pochette surgery with the trivial cord does not change the diffeomorphism type or gives a Gluck surgery. We also show that there exist pochette surgeries on the 4-sphere with a non-trivial core sphere and a non-trivial cord such that the surgeries give the 4-sphere.