# The Flow Completion of a Manifold with Vector Field

@inproceedings{Kamber2000TheFC, title={The Flow Completion of a Manifold with Vector Field}, author={Franz W. Kamber and Peter W. Michor}, year={2000} }

- Published 2000

For a vector field X on a smooth manifoldM there exists a smooth but not necessarily Hausdorff manifold MR and a complete vector field XR on it which is the universal completion of (M,X). 1. Theorem. Let X ∈ X(M) be a smooth vector field on a (connected) smooth manifold M . Then there exists a universal flow completion j : (M,X)→ (MR, XR) of (M,X). Namely, there exists a (connected) smooth not necessarily Hausdorff manifold MR, a complete vector field XR ∈ X(MR), and an embedding j : M →MR onto… CONTINUE READING