Infinite homotopy stable class for 4-manifolds with boundary

Anthony Conway, Diarmuid Crowley and Mark Powell

Vol. 325 (2023), No. 2, 209–237

DOI: 10.2140/pjm.2023.325.209

Abstract

We show that for every odd prime $q$, there exists an infinite family ${\{M_i\}}_{i=1}^{\infty }$ of topological 4-manifolds that are all stably homeomorphic to one another, all the manifolds $M_i$ have isometric rank one equivariant intersection pairings and boundary $L(2q,1)\#(S^1\times S^2)$, but they are pairwise not homotopy equivalent via any homotopy equivalence that restricts to a homotopy equivalence of the boundary.

Keywords

stable homeomorphism, homotopy equivalence, 4-manifold

Mathematical Subject Classification

Primary: 57K40, 57R65

Milestones

Received: 7 October 2022

Revised: 18 September 2023

Accepted: 20 September 2023

Published: 3 November 2023