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handle decomposition (Definition)

Let $ M^n$ be a smooth, connected, closed $ n$ dimensional manifold. A handle is $ H_{\lambda}^n = B^{\lambda} \times B^{n-\lambda}$ where $ B^{\lambda}$ is a $ \lambda$-ball.

Any such manifold $ M$ is diffeomorphic to the union of finitely many such handles where each handle $ H_{\lambda}^n$ is in a one-to-one correspondence with the critical points of index $ \lambda$ of a Morse function on $ M$.



"handle decomposition" is owned by RobKing.
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Cross-references: Morse function, critical points, one-to-one correspondence, union, diffeomorphic, manifold, closed, connected, smooth
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This is version 5 of handle decomposition, born on 2005-06-21, modified 2005-06-24.
Object id is 7180, canonical name is HandleDecomposition.
Accessed 1057 times total.

Classification:
AMS MSC: 57R19 (Manifolds and cell complexes :: Differential topology :: Algebraic topology on manifolds)
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