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Functions on Manifolds: Algebraic and Topological Aspects
 
Front Cover for Functions on Manifolds: Algebraic and Topological Aspects
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Hardcover ISBN: 978-0-8218-4578-3
Product Code: MMONO/131
List Price: $106.00
MAA Member Price: $95.40
AMS Member Price: $84.80
Electronic ISBN: 978-1-4704-4539-3
Product Code: MMONO/131.E
List Price: $100.00
MAA Member Price: $90.00
AMS Member Price: $80.00
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Front Cover for Functions on Manifolds: Algebraic and Topological Aspects
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  • Front Cover for Functions on Manifolds: Algebraic and Topological Aspects
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Functions on Manifolds: Algebraic and Topological Aspects
Available Formats:
Hardcover ISBN:  978-0-8218-4578-3
Product Code:  MMONO/131
List Price: $106.00
MAA Member Price: $95.40
AMS Member Price: $84.80
Electronic ISBN:  978-1-4704-4539-3
Product Code:  MMONO/131.E
List Price: $100.00
MAA Member Price: $90.00
AMS Member Price: $80.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $159.00
MAA Member Price: $143.10
AMS Member Price: $127.20
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 1311993; 193 pp
    MSC: Primary 57; 58;

    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.

  • Table of Contents
     
     
    • Chapters
    • Chapter I. Frechet manifolds
    • Chapter II. Minimal Morse functions on simply connected manifolds
    • Chapter III. Stable algebra
    • Chapter IV. Homotopy of chain complexes
    • Chapter V. Morse numbers and minimal Morse functions
    • Chapter VI. Elements of the homotopy theory of non-simply-connected CW-complexes
    • Chapter VII. Minimal Morse functions of non-simply-connected manifolds
    • Chapter VIII. Minimal round Morse functions
  • 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
  • Request Review Copy
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Volume: 1311993; 193 pp
MSC: Primary 57; 58;

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.

  • Chapters
  • Chapter I. Frechet manifolds
  • Chapter II. Minimal Morse functions on simply connected manifolds
  • Chapter III. Stable algebra
  • Chapter IV. Homotopy of chain complexes
  • Chapter V. Morse numbers and minimal Morse functions
  • Chapter VI. Elements of the homotopy theory of non-simply-connected CW-complexes
  • Chapter VII. Minimal Morse functions of non-simply-connected manifolds
  • Chapter VIII. Minimal round Morse functions
  • 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
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