Cocycle rigidity and splitting for some discrete parabolic actions

Danijela Damjanović; James Tanis

doi:10.3934/dcds.2014.34.5211

Article Contents

2014, Volume 34, Issue 12: 5211-5227. Doi: 10.3934/dcds.2014.34.5211

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Cocycle rigidity and splitting for some discrete parabolic actions

Danijela Damjanović^1, and
James Tanis^1,

1.
Department of Mathematics, Rice University, 6100 Main st, Houston, TX 77005

Received: August 31, 2013

Revised: April 30, 2014

Published: November 2014

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Abstract

We prove trivialization of the first cohomology with coefficients in smooth vector fields, for a class of $\mathbb{Z}^2$ parabolic actions on $(SL(2, \mathbb R)\times SL(2, \mathbb R))/\Gamma$, where the lattice $\Gamma$ is irreducible and co-compact. We also obtain a splitting construction involving first and second coboundary operators in the cohomology with coefficients in smooth vector fields.

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Mathematics Subject Classification: Primary: 37A20; Secondary: 37A15.

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