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The tubular neighborhood theorem November 5, 2009

Posted by Akhil Mathew in differential geometry, MaBloWriMo.
Tags: , , ,

If {M} is a manifold and {N} a compact submanifold, then a tubular neighborhood of {N} consists of an open set {U \supset N} diffeomorphic to a neighborhood of the zero section in some vector bundle {E} over {N}, by which N corresponds to the zero section.

Theorem 1 Hypotheses as above, {N} has a tubular neighborhood. (more…)