Bounded cohomology via partial differential equations, I

Hartnick, Tobias¹ ; Ott, Andreas²

¹ Mathematics Department, Technion, 32000 Haifa, Israel
² Mathematisches Institut, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 288, D-69120 Heidelberg, Germany

Geometry & topology, Tome 19 (2015) no. 6, pp. 3603-3643.

Résumé

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.

Détail

DOI : 10.2140/gt.2015.19.3603

Classification : 20J06, 22E41, 35F35
Keywords: bounded cohomology, Lie groups, partial differential equations

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