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 HandleDecomposition 2013-03-22 15:21:28 2013-03-22 15:21:28 RobKing (9598) RobKing (9598) 8 RobKing (9598) Definition msc 57R19