Vol. 310, No. 2, 2021

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$\mathbb{CP}^2$-stable classification of $4$-manifolds with finite fundamental group

Daniel Kasprowski and Peter Teichner

Vol. 310 (2021), No. 2, 355–373
DOI: 10.2140/pjm.2021.310.355
Abstract

We show that two closed, connected 4-manifolds with finite fundamental groups are 2-stably homeomorphic if and only if their quadratic 2-types are stably isomorphic and their Kirby–Siebenmann invariants agree.

Keywords
Whitehead's Gamma group, stable classification of 4-manifolds
Mathematical Subject Classification 2010
Primary: 57N13
Milestones
Received: 18 September 2019
Revised: 26 January 2020
Accepted: 30 November 2020
Published: 8 March 2021
Authors
Daniel Kasprowski
Mathematisches Institut
Rheinische Friedrich-Wilhelms-Universität Bonn
Bonn
Germany
Peter Teichner
Max Planck Institute for Mathematics
Bonn
Germany