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Infinite homotopy stable class for 4-manifolds with boundary

Anthony Conway, Diarmuid Crowley and Mark Powell

Vol. 325 (2023), No. 2, 209–237
Abstract

We show that for every odd prime q, there exists an infinite family {Mi}i=1 of topological 4-manifolds that are all stably homeomorphic to one another, all the manifolds Mi have isometric rank one equivariant intersection pairings and boundary L(2q,1)#(S1 × S2), 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
Authors
Anthony Conway
Department of Mathematics
University of Texas at Austin
Austin, TX
United States
Diarmuid Crowley
School of Mathematics & Statistics
University of Melbourne
Parkville, Vic
Australia
Mark Powell
School of Mathematics and Statistics
University of Glasgow
Glasgow
United Kingdom

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