Smooth and analytic actions of SL(n,\bf R) and SL(n,\bf Z) on closed n-dimensional manifolds

2022/10/18 by David E. Fisher, Fisher, David, Karin Melnick +1
Mathematics · #Advanced Algebra and Geometry #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2210.09516

openalex publication_date 2022/10/18 · openalex created_date 2022/10/21 · openalex updated_date 2026/07/28

Abstract

The main result is a classification of smooth actions of SL(n,\bf R), n ≥ 3, or connected groups locally isomorphic to it, on closed n-manifolds, extending a theorem of Uchida. We construct new exotic actions of SL(n,\bf Z) on the n-torus and connected sums of n-tori, and we formulate a conjectural classification of actions of lattices in SL(n,\bf R) on closed n-manifolds. We prove some results about invariant rigid geometric structures for SL(n,\bf R)-actions.

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