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Circle-valued Morse Theory

Circle-valued Morse Theory by Andrei V. Pajitnov
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In 1927 M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. It is a large and actively developing domain of differential topology, with applications and connections to many geometrical problems. The aim of the present book is to give a systematic treatment of the geometric foundations of a subfield of that topic, the circle-valued Morse functions, a subfield of Morse theory.

De Gruyter; January 2006
464 pages; ISBN 9783110197976
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Title: Circle-valued Morse Theory
Author: Andrei V. Pajitnov