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

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, ) in degree 4, establishing a special case of a conjecture of Monod.

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