Pochette surgery of 4-sphere

Tatsumasa Suzuki and Motoo Tange

Vol. 324 (2023), No. 2, 371–398

DOI: 10.2140/pjm.2023.324.371

Abstract

Iwase and Matsumoto (2004) defined “pochette surgery” as a cut-and-paste operation on 4-manifolds along a 4-manifold homotopy equivalent to $S^2\vee S^1$. Suzuki (2022) studied infinitely many homotopy 4-spheres obtained by pochette surgery. 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 nontrivial core sphere and a nontrivial cord such that the surgeries give the 4-sphere.

Keywords

4-manifolds, pochette surgery, handle calculus

Mathematical Subject Classification

Primary: 57K45, 57R65

Secondary: 57K40

Milestones

Received: 11 September 2022

Revised: 27 March 2023

Accepted: 6 May 2023

Published: 26 July 2023