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Topological $4$ -manifolds with right-angled Artin fundamental groups

Ian Hambleton

Department of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada

E-mail Address: hambleton@mcmaster.ca

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and

Alyson Hildum

Department of Mathematics & Computer Science, Wesleyan University, Middletown, CT 06459, USA

E-mail Address: ahildum@wesleyan.edu

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https://doi.org/10.1142/S1793525319500328Cited by:2 (Source: Crossref)

Abstract

We classify closed, spin $^{+}$ , topological $4$ -manifolds with fundamental group $π$ of cohomological dimension $\leq 3$ (up to $s$ -cobordism), after stabilization by connected sum with at most $b_{3} (π)$ copies of $S^{2} \times S^{2}$ . In general, we must also assume that $π$ 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 groupswhose defining graphs have no $4$ -cliques.

Keywords:

AMSC: 57N13, 57R65, 20F36

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