Space of group orderings, quasi morphisms and bounded cohomology

TL;DR

This paper explores the relationship between group orderings, quasi-morphisms, and bounded cohomology, revealing how these structures reflect properties of the group.

Contribution

It introduces a construction linking left orderings of a group to quasi-morphisms and bounded cohomology, providing new insights into their interplay.

Findings

Constructed a quasi-morphism from group orderings.

Established a map from orderings to second bounded cohomology.

Demonstrated how these maps reflect properties of group orderings.

Abstract

For a group $G$, we construct a quasi morphism from its left orderings and the map from the space of left orderings to the second bounded cohomology. We show that these maps reflect various properties of the group orderings.