Local freeness in frame bundle prolongations of C^∞ actions

2016/08/23 by Scot Adams, Adams, Scot
Mathematics · #53A55 #57Sxx #58A05 #58A20 #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1608.06595

openalex publication_date 2016/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G~be a real Lie group and let G^∘ be the identity component of~G. Let G~act on a C^∞ real manifold~M. Assume the action is C^∞. Assume that the fixpoint set of any nontrivial element of~G^∘ has empty interior in~M. Let n:=dim G. Assume n≥1. Let F be the frame bundle of~M of order n-1. We prove: there exists a G-invariant dense open subset~Q of~F such that the G-action on Q has discrete stabilizers.

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