Discrete free Abelian central stabilizers in a higher order frame bundle

Abstract

Let a real Lie group $G$ have a $C^{\infty }$ 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 $0$th, 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.

References in corpus (5)

• Real analytic counterexample to the freeness conjecture
• Freeness in higher order frame bundles
• Moving frames and prolongations of real algebraic actions
• Generic freeness in frame bundle prolongations of $C^{\infty }$ actions
• Local freeness in frame bundle prolongations of $C^{\infty }$ actions

Cited by in corpus (1)

• Generic freeness in frame bundle prolongations of $C^{\infty }$ actions