✦ LIBER ✦

Sofic groups and diophantine approximation

✍ Scribed by Andreas Thom

Publisher: John Wiley and Sons
Year: 2008
Tongue: English
Weight: 157 KB
Volume: 61
Category: Article
ISSN: 0010-3640
DOI: 10.1002/cpa.20217

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

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.

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