Infinite homotopy stable class for 4-manifolds with boundary

Abstract

We show that for every odd prime q, there exists an infinite family {M i } ∞ i=1 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 × S 2 ), but they are pairwise not homotopy equivalent via any homotopy equivalence that restricts to a homotopy equivalence of the boundary. MSC2020: 57K40, 57R65.