Totally non cohomologous to zero fibrations and amenable Clifford-Klein forms of 3-symmetric spaces

TL;DR

This paper proves that certain 3-symmetric spaces associated with simple real Lie groups cannot have amenable compact Clifford-Klein forms, using the concept of totally non cohomologous to zero fibrations.

Contribution

It introduces the use of totally non cohomologous to zero fibrations to study the existence of amenable Clifford-Klein forms in 3-symmetric spaces.

Findings

3-symmetric spaces of simple real Lie groups do not admit amenable compact Clifford-Klein forms

Utilizes totally non cohomologous to zero fibrations as a key tool

Provides new insights into the structure of Clifford-Klein forms in symmetric spaces

Abstract

We prove that 3-symmetric spaces of simple linear real Lie groups do not admit amenable compact Clifford-Klein forms. Our basic tool are totally non cohomologous to zero fibrations.