Sofic groups and diophantine approximation

By Andreas Thom. 2007

60 citations recorded by the source corpus.

We prove the algebraic eigenvalue conjecture of J. Dodziuk, P. Linnell, V. Mathai, T. Schick, and S. Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we define integer operators and prove a quantization of the operator norm below 2. To the knowledge of the author, there is no group known that is not sofic. © 2007 Wiley Periodicals, Inc.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5816bbdaf8b1fe5a371b595da1397182e40d95ab

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In Geometry and Topology

1. Valerio Capraro
2. Martino Lupini
3. William Slofstra

In Mathematical Physics

1. Valerio Capraro
2. Martino Lupini
3. William Slofstra

Citations in the corpus

• Introduction to Sofic and Hyperlinear Groups and Connes' Embedding Conjecture (2013, background): “The algebraic eigenvalues conjecture has been settled for sofic groups by Andreas Thom in [112].”