Group rings of three-manifold groups

2023/03/28 by Kielak, Dawid, Linton, Marco
#20J05 (Primary) #57K30 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2303.15907

Abstract

Let G be the fundamental group of a three-manifold. By piecing together many known facts about three manifold groups, we establish two properties of the group ring ℂG. We show that if G has rational cohomological dimension two, then ℂG is coherent. We also show that if G is torsion-free, then G satisfies the Strong Atiyah Conjecture over ℂ and hence that ℂG satisfies Kaplansky's Zero Divisor Conjecture.

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