A stability range for topological 4-manifolds

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 $S^2\times S^2$.

arXiv comment26 pages (v3). Revisions following referees' reports; final version, accepted for publication in Transactions of the American Mathematical Society

References in corpus (5)

• Stable classification of 4-manifolds with 3-manifold fundamental groups
• Four-manifolds up to connected sum with complex projective planes
• Topological 4-manifolds with right-angled Artin fundamental groups
• Cancellation for 4-manifolds with virtually abelian fundamental group
• ${\mathbb{CP}}^2$-stable classification of $4$-manifolds with finite fundamental group

Cited by in corpus (1)

• The Kervaire-Milnor invariant in the stable classification of spin 4-manifolds