Discrete free Abelian central stabilizers in a higher order frame bundle

Scot Adams

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arXiv · 1602.08460

Discrete free Abelian central stabilizers in a higher order frame bundle

Scot Adams

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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.

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BibTeX RIS

Scot Adams. 2016-02-26. Discrete free Abelian central stabilizers in a higher order frame bundle. https://arxiv.org/abs/1602.08460

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