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arXiv · 1608.06595

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

Scot Adams
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Abstract

Let $G$~be a real Lie group and let $G^\circ$ be the identity component of~$G$. Let $G$~act on a $C^\infty$ real manifold~$M$. Assume the action is $C^\infty$. Assume that the fixpoint set of any nontrivial element of~$G^\circ$ has empty interior in~$M$. Let $n:=\dim G$. Assume $n\ge1$. 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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Scot Adams. 2016-08-23. Local freeness in frame bundle prolongations of $C^\infty$ actions. https://arxiv.org/abs/1608.06595

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