Compact forms of homogeneous spaces and higher-rank semisimple group\n actions

2012/09/18 by David Constantine, Constantine, David
Computer Science · Mathematics · #22E40 #37D40 #53C30 #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1209.3940

openalex publication_date 2012/09/18 · openalex created_date 2022/09/02 · openalex updated_date 2026/07/28

Abstract

This paper proves that there are no compact forms for a large class of\nhomogeneous spaces admitting actions by higher-rank semisimple Lie groups. It\nbuilds on Zimmer's approach for studying such spaces using cocycle\nsuperrigidity. The proof involves cocycle superrigidity, measure rigidity for\nunipotent flows, techniques from partially hyperbolic dynamics, and the\ngeometry and pseudo-Riemannian structure of the homogeneous space.\n

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