#### Volume 19, issue 6 (2015)

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Bounded cohomology via partial differential equations, I

### Tobias Hartnick and Andreas Ott

Geometry & Topology 19 (2015) 3603–3643
##### Abstract

We present a new technique that employs partial differential equations in order to explicitly construct primitives in the continuous bounded cohomology of Lie groups. As an application, we prove a vanishing theorem for the continuous bounded cohomology of $SL\left(2,ℝ\right)$ in degree $4$, establishing a special case of a conjecture of Monod.

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##### Keywords
bounded cohomology, Lie groups, partial differential equations
##### Mathematical Subject Classification 2010
Primary: 20J06
Secondary: 22E41, 35F35