The strong Atiyah and Lück approximation conjectures for one-relator groups

It is shown that the strong Atiyah conjecture and the Lück approximation conjecture in the space of marked groups hold for locally indicable groups. In particular, this implies that one-relator groups satisfy both conjectures. We also show that the center conjecture, the independence conjecture and...

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Veröffentlicht in:	Mathematische annalen 2020-04, Vol.376 (3-4), p.1741-1793
Hauptverfasser:	Jaikin-Zapirain, Andrei, López-Álvarez, Diego
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Sprache:	eng
Schlagworte:	Algebra Approximation Eigenvalues Mathematical analysis Mathematics Mathematics and Statistics
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description	It is shown that the strong Atiyah conjecture and the Lück approximation conjecture in the space of marked groups hold for locally indicable groups. In particular, this implies that one-relator groups satisfy both conjectures. We also show that the center conjecture, the independence conjecture and the strong eigenvalue conjecture hold for these groups. As a byproduct we prove that the group algebra of a locally indicable group over a field of characteristic zero has a Hughes-free epic division algebra and, in particular, it is embedded in a division algebra.
doi_str_mv	10.1007/s00208-019-01926-0
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title	The strong Atiyah and Lück approximation conjectures for one-relator groups
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