A stability range for topological 4-manifolds

TL;DR

This paper introduces a new invariant for classifying closed, oriented topological 4-manifolds up to s-cobordism, using stabilization by connected sums with S^2×S^2, advancing understanding of their topological structure.

Contribution

It presents a novel stable range invariant that aids in the classification of 4-manifolds after stabilization, providing a new tool in topological manifold theory.

Findings

Defines a new stable range invariant for 4-manifolds

Establishes classification results up to s-cobordism

Shows the invariant's effectiveness after stabilization by S^2×S^2

Abstract

We introduce a new stable range invariant for the classification of closed, oriented topological $4$-manifolds (up to $s$-cobordism), after stabilization by connected sum with a uniformly bounded number of copies of $S^2\times S^2$.