2016/02/26 by Scot Adams, Adams, Scot · 1 citation
Mathematics · Physics and Astronomy · #Homotopy and Cohomology in Algebraic Topology #Algebraic Geometry and Number Theory #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1602.08460
Let a real Lie group G have a C^∞ action on a real manifold M. Assume every nontrivial element of G has nowhere dense fixpoint set in M. First, we show, in every frame bundle, except possibly the 0th, that each stabilizer admits no nontrivial compact subgroups. Second, we show that, if G is connected, then there is a dense open G-invariant subset of some higher order frame bundle of M such that, for any point x in that subset, the stabilizer in G of x is a discrete, finitely-generated, free-Abelian, central subgroup of G. We derive several corollaries of these two results.