naa a22 4500 510781306 CHVBK 20180411083248.0 cr unu---uuuuu 180411e20131001xx s 000 0 eng 10.1007/s11854-013-0032-z doi (NATIONALLICENCE)springer-10.1007/s11854-013-0032-z Ramírez F. Department of Mathematics, University of York, YO10 5DD, York, UK aut Higher cohomology for Anosov actions on certain homogeneous spaces [Elektronische Daten] [F. Ramírez] We study the smooth untwisted cohomology with real coefficients for the action on [SL(2,ℝ)× ×SL(2,ℝ)]/Γ by the subgroup of diagonal matrices, where Γ is an irreducible lattice. We show that in the top degree, the obstructions to solving the coboundary equation come from distributions that are invariant under the action. We also show that in intermediate degrees, the cohomology trivializes. It has been conjectured by A. Katok and S. Katok that, analogously to Livšic's theorem for Anosov flows for a standard partially hyperbolic ℝ d - or ℤ d - action, the obstructions to solving the top-degree coboundary equation are given by periodic orbits, and also that the intermediate cohomology trivializes, as it is known to do in the first degree by work of Katok and Spatzier. Katok and Katok proved their conjecture for abelian groups of toral automorphisms. Our results verify the "intermediate cohomology” part of the conjecture for diagonal subgroup actions on SL(2,ℝ) d /Γ and are a step in the direction of the "top-degree cohomology” part. Hebrew University Magnes Press, 2013 Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 177-222 0021-7670 121:1<177 2013 121 11854 https://doi.org/10.1007/s11854-013-0032-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11854-013-0032-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ramírez F. Department of Mathematics, University of York, YO10 5DD, York, UK aut NATIONALLICENCE 773 0- Journal d'Analyse Mathématique Springer US; http://www.springer-ny.com 121/1(2013-10-01), 177-222 0021-7670 121:1<177 2013 121 11854 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer