Stable classification of 4-manifolds with 3-manifold fundamental groups

TL;DR

This paper classifies certain 4-manifolds with 3-manifold fundamental groups up to stable diffeomorphism using algebraic invariants, providing explicit criteria for spin cases.

Contribution

It establishes a complete stable classification of these 4-manifolds based on their w_2-type and equivariant intersection forms, including explicit invariants for spin manifolds.

Findings

Stable diffeomorphism characterized by w_2-type and intersection forms

Explicit algebraic invariants for spin manifolds

Classification results for 4-manifolds with 3-manifold fundamental groups

Abstract

We study closed, oriented 4-manifolds whose fundamental group is that of a closed, oriented, aspherical 3-manifold. We show that two such 4-manifolds are stably diffeomorphic if and only if they have the same w_2-type and their equivariant intersection forms are stably isometric. We also find explicit algebraic invariants that determine the stable classification for spin manifolds in this class.