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arXiv · 1605.06527

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

Scot Adams
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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.

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Scot Adams. 2016-05-20. Generic freeness in frame bundle prolongations of $C^\infty$ actions. https://arxiv.org/abs/1605.06527

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