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Product Code:  MMONO/124.S 
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Softcover ISBN:  9780821891643 
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Softcover ISBN:  9780821891643 
Product Code:  MMONO/124.S 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9781470445324 
Product Code:  MMONO/124.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821891643 
eBook ISBN:  9781470445324 
Product Code:  MMONO/124.S.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: 124; 1993; 183 ppMSC: Primary 57; Secondary 58;
This book covers fundamental techniques in the theory of \(C^{\infty }\)imbeddings and \(C^{\infty }\)immersions, emphasizing clear intuitive understanding and containing many figures and diagrams. Adachi starts with an introduction to the work of Whitney and of Haefliger on \(C^{\infty }\)imbeddings and \(C^{\infty }\)manifolds. The SmaleHirsch theorem is presented as a generalization of the classification of \(C^{\infty }\)imbeddings by isotopy and is extended by Gromov's work on the subject, including Gromov's convex integration theory. Finally, as an application of Gromov's work, the author introduces Haefliger's classification theorem of foliations on open manifolds. Also described here is the Adachi's work with Landweber on the integrability of almost complex structures on open manifolds. This book would be an excellent text for upperdivision undergraduate or graduate courses.
ReadershipResearch mathematicians and graduate students.

Table of Contents

Chapters

Chapter 0. Regular closed curves in the plane

Chapter I. $C^r$ manifolds, $C^r$ maps, and fiber bundles

Chapter II. Embeddings of $C^\infty $ manifolds

Chapter III. Immersions of $C^\infty $ manifolds

Chapter IV. The Gromov convex integration theory

Chapter V. Foliations of open manifolds

Chapter VI. Complex structures on open manifolds

Chapter VII. Embeddings of $C^\infty $ manifolds (continued)


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This book covers fundamental techniques in the theory of \(C^{\infty }\)imbeddings and \(C^{\infty }\)immersions, emphasizing clear intuitive understanding and containing many figures and diagrams. Adachi starts with an introduction to the work of Whitney and of Haefliger on \(C^{\infty }\)imbeddings and \(C^{\infty }\)manifolds. The SmaleHirsch theorem is presented as a generalization of the classification of \(C^{\infty }\)imbeddings by isotopy and is extended by Gromov's work on the subject, including Gromov's convex integration theory. Finally, as an application of Gromov's work, the author introduces Haefliger's classification theorem of foliations on open manifolds. Also described here is the Adachi's work with Landweber on the integrability of almost complex structures on open manifolds. This book would be an excellent text for upperdivision undergraduate or graduate courses.
Research mathematicians and graduate students.

Chapters

Chapter 0. Regular closed curves in the plane

Chapter I. $C^r$ manifolds, $C^r$ maps, and fiber bundles

Chapter II. Embeddings of $C^\infty $ manifolds

Chapter III. Immersions of $C^\infty $ manifolds

Chapter IV. The Gromov convex integration theory

Chapter V. Foliations of open manifolds

Chapter VI. Complex structures on open manifolds

Chapter VII. Embeddings of $C^\infty $ manifolds (continued)