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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Published in | Transformation groups Vol. 23; no. 4; pp. 893 - 913 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
New York
Springer US
01.12.2018
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 1083-4362 1531-586X |
DOI: | 10.1007/s00031-017-9463-4 |