Bounded cohomology via partial differential equations, I

Hartnick, Tobias; Ott, Andreas

doi:10.2140/gt.2015.19.3603

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Bounded cohomology via partial differential equations, I

Tobias Hartnick and Andreas Ott

Geometry & Topology 19 (2015) 3603–3643

DOI: 10.2140/gt.2015.19.3603

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 $SL (2, ℝ)$ 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

References

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

Volume 19, issue 6 (2015)