Circle-valued Morse Theory : Circle-valued Morse Theory.
Title:
Circle-valued Morse Theory : Circle-valued Morse Theory.
Author:
Pajitnov, Andrei V.
ISBN:
9783110197976
Personal Author:
Physical Description:
1 online resource (454 pages)
Series:
De Gruyter Studies in Mathematics ; v.32
De Gruyter Studies in Mathematics
Contents:
Contents -- Preface -- Introduction -- Part 1Morse functions and vector fieldson manifolds -- CHAPTER 1Vector fields and C0 topology -- CHAPTER 2Morse functions and their gradients -- CHAPTER 3Gradient flows of real-valued Morse functions -- CHAPTER 4The Kupka-Smale transversality theory forgradient flows -- CHAPTER 5Handles -- CHAPTER 6The Morse complex of a Morse function -- History and Sources -- Part 3Cellular gradients. -- CHAPTER 7Condition (C) -- CHAPTER 8Cellular gradients are C0-generic -- CHAPTER 9Properties of cellular gradients -- Sources -- Part 4Circle-valued Morse maps andNovikov complexes -- CHAPTER 10Completions of rings, modules and complexes -- CHAPTER 11The Novikov complex of a circle-valued Morsemap -- CHAPTER 12Cellular gradients of circle-valued Morsefunctions and the Rationality Theorem -- CHAPTER 13Counting closed orbits of the gradient flow -- CHAPTER 14Selected topics in the Morse-Novikov theory -- History and Sources -- Bibliography -- Selected Symbols and Abbreviations -- Subject Index.
Abstract:
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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Genre:
Electronic Access:
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