Cocycle rigidity and splitting for some discrete parabolic actions

James Tanis, Danijela Damjanović
2014 Discrete and Continuous Dynamical Systems. Series A  
We prove trivialization of the first cohomology with coefficients in smooth vector fields, for a class of Z 2 parabolic actions on (SL(2, R) × SL(2, R))/Γ, where the lattice Γ 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. 2010 Mathematics Subject Classification. Primary: 37A20; Secondary: 37A15.
doi:10.3934/dcds.2014.34.5211 fatcat:2ya5y44pyng2pamrlh3xsrn24q