Topological 4-manifolds with right-angled Artin fundamental groups

Abstract

We classify closed, topological spin${}^{+}$ 4-manifolds with fundamental group $\pi$ of cohomological dimension $\le 3$ (up to s-cobordism), after stabilization by connected sum with at most $b_3(\pi )$ copies of $S^2\times S^2$. In general we must also assume that $\pi$ also satisfies certain K-theory and assembly map conditions. Examples for which these conditions hold include the torsion-free fundamental groups of 3-manifolds and all right-angled Artin groups whose defining graphs have no 4-cliques.

39 pages. This is the final version. References have been updated

References in corpus (2)

• Stable classification of 4-manifolds with 3-manifold fundamental groups
• The minimum $b_2$ problem for right-angled Artin groups

Cited by in corpus (5)

• A survey of the foundations of four-manifold theory in the topological category
• Algebraic criteria for stable diffeomorphism of spin 4-manifolds
• Stable diffeomorphism classification of some unorientable 4-manifolds
• A stability range for topological 4-manifolds
• Four-manifolds, two-complexes and the quadratic bias invariant