Topological 4-manifolds with right-angled Artin fundamental groups
Ian Hambleton, Alyson Hildum

TL;DR
This paper classifies certain 4-manifolds with specific fundamental groups, using stabilization and algebraic conditions, expanding understanding of their topological and geometric structures.
Contribution
It provides a classification of topological spin$^+$ 4-manifolds with right-angled Artin fundamental groups under specific algebraic and topological conditions.
Findings
Classification up to s-cobordism after stabilization
Applicable to torsion-free 3-manifold groups and certain RAAGs
Conditions involve K-theory and assembly maps
Abstract
We classify closed, topological spin 4-manifolds with fundamental group of cohomological dimension (up to s-cobordism), after stabilization by connected sum with at most copies of . In general we must also assume that 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.
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