nLab G-manifold (Rev #3, changes)

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For $G$ a Lie group, by a $G$-manifold one may mena

• a smooth manifold with $G$-special holonomy;

• a smooth manifold equipped with a smooth group action by $G$

  (the smooth version of a topological G-space, see also at equivariant differential topologyequivariant differential topology)