Finitely generated simple left orderable groups with vanishing second bounded cohomology

Abstract

We prove that the finitely generated simple left orderable groups constructed by the second author with Hyde have vanishing second bounded cohomology, both with trivial real and trivial integral coefficients. As a consequence, these are the first examples of finitely generated non-indicable left orderable groups with vanishing second bounded cohomology. This answers Question 8 from the 2018 ICM proceedings article of Andrés Navas.

arXiv comment18 pages. The content of this preprint has been moved to another paper of the authors: arXiv:2111.07931