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The flow completion of a manifold with vector field. (English) Zbl 0955.37007

Summary: For a vector field \(X\) on a smooth manifold \(M\) there exists a smooth but not necessarily Hausdorff manifold \(M_{\mathbb{R}}\) and a complete vector field \(X_{\mathbb{R}}\) on it which is the universal completion of \((M,X)\).

MSC:

37C10 Dynamics induced by flows and semiflows
57R30 Foliations in differential topology; geometric theory
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References:

[1] D. V. Alekseevsky and Peter W. Michor, Differential geometry of \?-manifolds, Differential Geom. Appl. 5 (1995), no. 4, 371 – 403. · Zbl 0854.53028 · doi:10.1016/0926-2245(95)00023-2
[2] F. W. Kamber and P. W. Michor, Completing Lie algebra actions to Lie group actions, in preparation. · Zbl 1066.22021
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