arXiv subjects
Publications and source records attributed to E. Szabo.
We consider rationally connected complex projective manifolds M and show that their loop spaces--infinite dimensional complex manifolds--have properties similar to those of M. Furthermore, we give a finite dimensional application concerning holomorphic vector bundles over rationally connected complex projective manifolds.
We construct an analogue of Neumann's affiliated algebras for sofic group algebras over arbitrary fields. Consequently, we settle Kaplansky's direct finiteness conjecture for sofic groups.
Answering some queries of Weiss, we prove that the free product and amenable extensions of sofic groups are sofic as well, and give an example of a finitely generated sofic group that is not residually amenable.