Contractibility of the automorphism group of a von Neumann algebra

TL;DR

This paper proves that the automorphism group of certain von Neumann algebras, including the hyperfinite type III_1 factor, is contractible in the u-topology, revealing topological simplicity.

Contribution

It establishes the contractibility of the automorphism group for a class of von Neumann algebras, including the hyperfinite type III_1 factor, in the u-topology.

Findings

Automorphism group of a separable strongly stable von Neumann algebra is contractible.

The automorphism group of the hyperfinite type III_1 factor is contractible.

Contractibility holds in the u-topology.

Abstract

We prove that the approximately inner automorphism group of a separable strongly stable von Neumann algebra is contractible in the u-topology. Thus the automorphism group of the hyperfinite type III_1 factor is contractible.