PROLONGED ANALYTIC CONNECTED GROUP ACTIONS ARE GENERICALLY FREE

We prove that an effective, analytic action of a connected Lie group G on an analytic manifold M becomes free on a comeager subset of an open subset of M when prolonged to a frame bundle of sufficiently high order. We further prove that the action of G becomes free on a comeager subset of an open su...

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Bibliographic Details
Published inTransformation groups Vol. 23; no. 4; pp. 893 - 913
Main Authors ADAMS, SCOT, OLVER, PETER J.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2018
Springer Nature B.V
Subjects
Algebra
Differential equations
Lie Groups
Manifolds (mathematics)
Mathematical analysis
Mathematics
Mathematics and Statistics
Topological Groups
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Summary:We prove that an effective, analytic action of a connected Lie group G on an analytic manifold M becomes free on a comeager subset of an open subset of M when prolonged to a frame bundle of sufficiently high order. We further prove that the action of G becomes free on a comeager subset of an open subset of a submanifold jet bundle over M of sufficiently high order, thereby establishing a general result that underlies Lie's theory of symmetry groups of differential equations and the equivariant method of moving frames.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-017-9463-4