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

Abstract

Let a real Lie group $G$ act on a $C^{\infty }$ real manifold $M$. Assume that the action is $C^{\infty }$ and that every nontrivial element of $G$ has a nowhere dense fixpoint set in $M$. We show that, in~some higher order frame bundle $F$ of $M$, there exists a $G$-invariant meager subset $Z$ of $F$ such that the $G$-action on $F\backslash Z$ is free. A similar result holds for submanifold jet bundles.

References in corpus (3)

• Real analytic counterexample to the freeness conjecture
• Freeness in higher order frame bundles
• Discrete free Abelian central stabilizers in a higher order frame bundle

Cited by in corpus (1)

• Discrete free Abelian central stabilizers in a higher order frame bundle