Group rings of three-manifold groups
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Publication:6431115
DOI10.1090/PROC/16716arXiv2303.15907OpenAlexW4389040615MaRDI QIDQ6431115
Publication date: 28 March 2023
Abstract: We show that finitely generated fundamental groups of three-manifolds satisfy the Strong Atiyah Conjecture over the complex numbers. This implies that when the group is additionally torsion-free, then its complex group ring satisfies the Kaplansky Zero-divisor Conjecture. As an application, we give a very short proof of a significant generalisation of a recent result of Shalen dealing with the minimal index of freedom of three-manifold groups.
Full work available at URL: https://doi.org/10.1090/proc/16716
Homological methods in group theory (20J05) Fundamental groups and their automorphisms (group-theoretic aspects) (20F34) General topology of 3-manifolds (57K30)
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