Abstract
The action \(\Phi :{\kern 1pt} \,\;G \times M \to M\) of Lie group G on a manifold M can be seen as the choice of a subgroup \({A_G}: = \{ {\Phi _g}|g \in G\}\) of Diff(M), that is, the globally defined diffeomorphisms of M. There are mathematical structures, such as distributions and foliations, where the transformations of the manifold M that naturally appear in the problem are only locally defined. It is in the study of those structures that the objects constituting the subject of this chapter become relevant.
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© 2004 Juan Pablo Ortega and Tudor S. Ratiu
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Ortega, JP., Ratiu, T.S. (2004). Pseudogroups and Groupoids. In: Momentum Maps and Hamiltonian Reduction. Progress in Mathematics, vol 222. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-3811-7_3
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DOI: https://doi.org/10.1007/978-1-4757-3811-7_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4757-3813-1
Online ISBN: 978-1-4757-3811-7
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