Compact group Rohlin actions and $G$-kernels on von Neumann algebras

TL;DR

This paper introduces a new topological group model for the string group of certain Lie groups, utilizing the obstruction realization problem and Rohlin property to establish cohomology vanishing results.

Contribution

It provides a novel construction of a topological group model for the string group via solving the obstruction realization problem for compact group G-kernels on full factors.

Findings

Constructed a new topological group model for the string group.

Established cohomology vanishing theorems using Rohlin property.

Solved the obstruction realization problem for G-kernels on full factors.

Abstract

We provide a new construction of a topological group model for the string group of a compact, simple, and simply-connected Lie group, by solving the obstruction realization problem for compact group $G$-kernels on full factors. Furthermore, we introduce the Rohlin property for actions and cocycle actions of compact groups in order to establish cohomology vanishing theorems.