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The flow completion of a manifold with vector field

Authors: Franz W. Kamber and Peter W. Michor
Journal: Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 95-97
MSC (2000): Primary 37C10, 57R30
Published electronically: October 10, 2000
MathSciNet review: 1783093
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Abstract: 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 $(M,X)$.

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Additional Information

Franz W. Kamber
Affiliation: Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801

Peter W. Michor
Affiliation: Institut für Mathematik, Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria; and: Erwin Schrödinger Institut für Mathematische Physik, Boltzmanngasse 9, A-1090 Wien, Austria
MR Author ID: 124340

Keywords: Flow completion, non-Hausdorff manifolds
Received by editor(s): July 27, 2000
Published electronically: October 10, 2000
Additional Notes: Supported by Erwin Schrödinger International Institute of Mathematical Physics, Wien, Austria. FWK was supported in part by The National Science Foundation under Grant No. DMS-9504084. PWM was supported by ‘Fonds zur Förderung der wissenschaftlichen Forschung, Projekt P 14195 MAT’
Communicated by: Alexandre Kirillov
Article copyright: © Copyright 2000 American Mathematical Society