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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Locally free affine group actions


Author: J. F. Plante
Journal: Trans. Amer. Math. Soc. 259 (1980), 449-456
MSC: Primary 57S20
DOI: https://doi.org/10.1090/S0002-9947-1980-0567090-9
MathSciNet review: 567090
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Abstract: Differentiable actions by the nonabelian 2-dimensional Lie group on compact manifolds are considered. When the action is locally free and the orbits have codimension one it is shown that there are at most finitely many minimal sets each containing a countably infinite number of cylindrical orbits. Examples are given to show that various codimension, differentiability, and minimality restrictions are necessary.


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DOI: https://doi.org/10.1090/S0002-9947-1980-0567090-9
Keywords: Lie group actions, orbits, minimal sets, flows, invariant measures, contraction
Article copyright: © Copyright 1980 American Mathematical Society