handle decomposition

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 $\lambda$ of a Morse function on $M$.

Title	handle decomposition
Canonical name	HandleDecomposition
Date of creation	2013-03-22 15:21:28
Last modified on	2013-03-22 15:21:28
Owner	RobKing (9598)
Last modified by	RobKing (9598)
Numerical id	8
Author	RobKing (9598)
Entry type	Definition
Classification	msc 57R19