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- Title
Vanishing first cohomology and strong 1-boundedness for von Neumann algebras.
- Authors
Hayes, Ben; Jekel, David; Elayavalli, Srivatsav Kunnawalkam
- Abstract
We obtain a new proof of Shlyakhtenko's result which states that if G is a sofic, finitely presented group with vanishing first '2-Betti number, then L.G/is strongly 1-bounded. Our proof of this result adapts and simplifies Jung's technical arguments which showed strong 1-boundedness under certain conditions on the Fuglede-Kadison determinant of the matrix capturing the relations. Our proof also features a key idea due to Jung which involves an iterative estimate for the covering numbers of microstate spaces. We also use the works of Shlyakhtenko and Shalom to give a short proof that the von Neumann algebras of sofic groups with Property (T) are strongly 1 bounded, which is a special case of another result by the authors.
- Subjects
VON Neumann, John, 1903-1957; GROUP algebras; VON Neumann algebras; BETTI numbers
- Publication
Journal of Noncommutative Geometry, 2024, Vol 18, Issue 2, p383
- ISSN
1661-6952
- Publication type
Article
- DOI
10.4171/JNCG/530