| Résume | Since the trailblazing paper of Gromov of 82, bounded cohomology has matured into a powerful tool to understand metric and geometrical properties of several interesting spaces. Still, typically the information obtained consists of whether the second bounded cohomology group is finite or infinite dimensional or not; somewhat surprisingly, this is enough for the referred applications.
On the other hand, there is no concrete description of what this vector space actually is. Together with Federico Rodriguez-Hertz (PSU) we started investigating this problem using methods of dynamical systems, particularly thermodynamic formalism. Due to this, our techniques work naturally well in spaces whether a priori there is some dynamical process, for example hyperbolic groups, and perhaps isometry groups of more general spaces with some hyperbolicity. In this talk I'm going to describe what we have been doing, results and future problems. |
