Geometry & Topology

Bounded cohomology via partial differential equations, I

Tobias Hartnick and Andreas Ott

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

Article information

Source
Geom. Topol., Volume 19, Number 6 (2015), 3603-3643.

Dates
Received: 11 October 2014
Accepted: 20 April 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1510858882

Digital Object Identifier
doi:10.2140/gt.2015.19.3603

Mathematical Reviews number (MathSciNet)
MR3447111

Zentralblatt MATH identifier
1335.22013

Subjects
Primary: 20J06: Cohomology of groups
Secondary: 22E41: Continuous cohomology [See also 57R32, 57Txx, 58H10] 35F35: Linear first-order systems

Keywords
bounded cohomology Lie groups partial differential equations

Citation

Hartnick, Tobias; Ott, Andreas. Bounded cohomology via partial differential equations, I. Geom. Topol. 19 (2015), no. 6, 3603--3643. doi:10.2140/gt.2015.19.3603. https://projecteuclid.org/euclid.gt/1510858882


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