Hardcover ISBN:  9780821845783 
Product Code:  MMONO/131 
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eBook ISBN:  9781470445393 
Product Code:  MMONO/131.E 
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AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845783 
eBook: ISBN:  9781470445393 
Product Code:  MMONO/131.B 
List Price:  $320.00 $242.50 
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AMS Member Price:  $256.00 $194.00 
Hardcover ISBN:  9780821845783 
Product Code:  MMONO/131 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445393 
Product Code:  MMONO/131.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Hardcover ISBN:  9780821845783 
eBook ISBN:  9781470445393 
Product Code:  MMONO/131.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 131; 1993; 193 ppMSC: 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 nonsimplyconnected 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.
ReadershipGraduate students, postgraduate 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 nonsimplyconnected CWcomplexes

Chapter VII. Minimal Morse functions of nonsimplyconnected 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


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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 nonsimplyconnected 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.
Graduate students, postgraduate 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 nonsimplyconnected CWcomplexes

Chapter VII. Minimal Morse functions of nonsimplyconnected 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