$\mathbb{CP}^2$-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 ${ℂ\mathbb{P}}^2$-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