# Second bounded cohomology and WWPD

## TL;DR

This paper explores the second bounded cohomology of groups acting on hyperbolic spaces, extending the study from WPD to the more general WWPD property introduced by Bestvina, Bromberg, and Fujiwara.

## Contribution

It generalizes the analysis of second bounded cohomology by utilizing the WWPD property, broadening the scope beyond the WPD condition.

## Key findings

- Established new connections between WWPD and second bounded cohomology.
- Extended the applicability of bounded cohomology techniques to broader group actions.
- Provided foundational results for future research on hyperbolic group actions.

## Abstract

Given a group acting on a Gromov hyperbolic space, Bestvina and Fujiwara introduced the WPD property --- weak proper discontinuity --- for studying the 2nd bounded cohomology of the group. We carry out a more general study of second bounded cohomology using a 'really' weak property discontinuity property known as WWPD that was introduced by Bestvina, Bromberg, and Fujiwara.