Separating submanifold: Difference between revisions
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(In fact much weaker assumptions that simple connectedness suffice; all we need is that the first homology has no 2-torsion). | (In fact much weaker assumptions that simple connectedness suffice; all we need is that the first homology has no 2-torsion). | ||
Revision as of 00:50, 3 December 2007
This article defines a property of a submanifold inside a manifold
Definition
A submanifold of a connected manifold is termed separating if it has codimension 1, and if its complement in the manifold is disconnected.
Facts
- In a simply connected manifold, any compact connected submanifold of codimension one, is separating. For full proof, refer: compact connected implies separating in simply connected
(In fact much weaker assumptions that simple connectedness suffice; all we need is that the first homology has no 2-torsion).