In this talk I will describe some new results around the second bounded cohomology of various finitely generated and finitely presented groups acting on the line. This leads to the solution (in the negative) of the following question of Navas: Does the vanishing of second bounded cohomology (with trivial real coefficients) imply indicability of a finitely generated left orderable group? This is joint work with Fournier-Facio
https://indico.math.cnrs.fr/event/7399/