Bounded cohomology via partial differential equations. I (Q906191)

The aim of this paper is to develop a new approach to the construction of primitives in continuous bounded cohomology for real semisimple Lie groups \(G\). The new technique presented by the authors for the explicit construction of primitives employs partial differential equations. As an application they prove a vanishing theorem for the continuous bounded cohomology of \(\mathrm{SL}(2, \mathbb R)\) in degree \(4\). To demonstrate this the authors reformulate the problem of constructing bounded primitives in terms of a fixed point problem for the action of \(G\) on a certain function space. The main idea is then to describe the fixed points as solutions of a certain system of linear first-order partial differential equations.