Infinite homotopy stable class for 4-manifolds with boundary

Conway, A., Crowley, D. and Powell, M. (2023) Infinite homotopy stable class for 4-manifolds with boundary. Pacific Journal of Mathematics, 325(2), pp. 209-237. (doi: 10.2140/pjm.2023.325.209)

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.

• Item Type: Articles
• Additional Information: Conway was partially supported by the NSF Standard Grant DMS-2303674. Powell was partially supported by the EPSRC New Investigator grant EP/T028335/2 and EPSRC New Horizons grant EP/V04821X/2.
• Keywords: Stable homeomorphism, homotopy equivalence, 4-manifold
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Powell, Professor Mark
• Authors: Conway, A., Crowley, D., and Powell, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Pacific Journal of Mathematics
• Publisher: Mathematical Sciences Publisher
• ISSN: 0030-8730
• ISSN (Online): 0030-8730
• Copyright Holders: Copyright: © 2023 The Authors
• First Published: First published in Pacific Journal of Mathematics 325(2): 209-237
• Publisher Policy: Reproduced under a Creative Commons licence

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
320615		Symmetries of 4-manifolds	Mark Powell	Engineering and Physical Sciences Research Council (EPSRC)	EP/V04821X/2	M&S - Mathematics
320909		Classifying 4-manifolds	Mark Powell	Engineering and Physical Sciences Research Council (EPSRC)	EP/T028335/2	M&S - Mathematics