The strong Atiyah and L\"uck approximation conjectures for one-relator groups
Group Theory
2019-11-12 v4
Abstract
It is shown that the strong Atiyah conjecture and the L\"uck 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.
Cite
@article{arxiv.1810.12135,
title = {The strong Atiyah and L\"uck approximation conjectures for one-relator groups},
author = {Andrei Jaikin-Zapirain and Diego López-Álvarez},
journal= {arXiv preprint arXiv:1810.12135},
year = {2019}
}
Comments
Corrected typos