Handle Decomposition
978-613-4-35412-7
6134354120
72
2011-02-28
29.00 €
eng
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a handle decomposition of an m-manifold M is a union emptyset = M_{-1} subset M_0 subset M_1 subset M_2 subset dots subset M_{m-1} subset M_m = M where each Mi is obtained from Mi − 1 by the attaching of i-handles. A handle decomposition is to a manifold what a CW-decomposition is to a topological space—in many regards the purpose of a handle decomposition is to have a language analogous to CW-complexes, but adapted to the world of smooth manifolds. Thus an i-handle is the smooth analogue of an i-cell. Handle decompositions of manifolds arise naturally via Morse theory. The modification of handle structures is closely linked to Cerf theory.
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