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
DOI:
https://doi.org/10.1090/S1079-6762-00-00083-4
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 $(M,X)$.
[1]1 D. V. Alekseevsky and Peter W. Michor, Differential geometry of $\mathfrak {g}$-manifolds., Differ. Geom. Appl. 5 (1995), 371–403, math.DG/9309214.
[2]2 F. W. Kamber and P. W. Michor, Completing Lie algebra actions to Lie group actions, in preparation.
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Additional Information
Franz W. Kamber
Affiliation:
Department of Mathematics, University of Illinois, 1409 West Green Street, Urbana, IL 61801
Email:
kamber@math.uiuc.edu
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
Email:
michor@pap.univie.ac.at
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