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Functions on Manifolds: Algebraic and Topological Aspects
V. V. Sharko
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Translations of Mathematical Monographs
1993; 193 pp; hardcover
Volume: 131
ISBN-10: 0-8218-4578-0
ISBN-13: 978-0-8218-4578-3
List Price: US$95
Member Price: US$76
Order Code: MMONO/131
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This monograph covers in a unified manner new results on smooth functions on manifolds. A major topic is Morse and Bott functions with a minimal number of singularities on manifolds of dimension greater than five. Sharko computes obstructions to deformation of one Morse function into another on a simply connected manifold. In addition, a method is developed for constructing minimal chain complexes and homotopical systems in the sense of Whitehead. This leads to conditions under which Morse functions on non-simply-connected manifolds exist. Sharko also describes new homotopical invariants of manifolds, which are used to substantially improve the Morse inequalities. The conditions guaranteeing the existence of minimal round Morse functions are discussed.

Readership

Graduate students, post-graduate students, topologists, and algebraists.

Reviews

"This book is tightly written ... contains a wealth of information on the topological and algebraic apparatus necessary for the construction of minimal Morse functions."

-- Mathematical Reviews

"Clear, concise and readable style ... should prove to be an important contribution."

-- Bulletin of the London MathematicalSociety

"The translation and the printing are faultless."

-- Zentralblatt MATH

Table of Contents

  • Fréchet manifolds
  • Minimal Morse functions on simply connected manifolds
  • Stable algebra
  • Homotopy of chain complexes
  • Morse numbers and minimal Morse functions
  • Elements of the homotopy theory of non-simply-connected CW-complexes
  • Minimal Morse functions of non-simply-connected manifolds
  • Minimal round Morse functions
  • Bibliography
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