handle decomposition

Let Mn be a smooth, connected, closed n dimensional manifoldMathworldPlanetmath. A handle is Hλn=Bλ×Bn-λ where Bλ is a λ-ball.

Any such manifold M is diffeomorphic to the union of finitely many such handles where each handle Hλn is in a one-to-one correspondence with the critical points of λ 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