Abstract

Starting with the work of Gromov on Gottschalk’s Surjunctivity Conjecture, the class of sofic groups has attracted much interest in various areas of mathematics. Major applications of this notion arose in the work Elek and Szabo on Kaplansky’s Direct Finiteness Conjecture, Lück’s Determinant Conjecture, and more recently in joint work with Klyachko on generalizations of the Kervaire-Laudenbach Conjecture and Howie’s Conjecture. Despite considerable effort, no non-sofic group has been found so far. In view of this situation, attempts have been made to provide variations of the problem that might be more approachable. Using the seminal work of Nikolov-Segal, we prove that the topological group SO(3) is not weakly sofic and describe the class of discrete groups that is approximable by finite solvable groups. (This is joint work with Jakob Schneider and Nikolay Nikolov.)