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

 Download this article For screen For printing
 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
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.

##### Keywords
bounded cohomology, Lie groups, partial differential equations
##### Mathematical Subject Classification 2010
Primary: 20J06
Secondary: 22E41, 35F35
##### Publication
Received: 11 October 2014
Accepted: 20 April 2015
Published: 6 January 2016
Proposed: Danny Calegari
Seconded: Leonid Polterovich, Jesper Grodal
##### Authors
 Tobias Hartnick Mathematics Department Technion 32000 Haifa Israel Andreas Ott Mathematisches Institut Ruprecht-Karls-Universität Heidelberg Im Neuenheimer Feld 288 D-69120 Heidelberg Germany