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Embeddings and Immersions
Masahisa Adachi

Translations of Mathematical Monographs
1993; 183 pp; softcover
Volume: 124
ISBN-10: 0-8218-9164-2
ISBN-13: 978-0-8218-9164-3
List Price: US$90
Member Price: US$72
Order Code: MMONO/124.S
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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 Smale-Hirsch 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 upper-division undergraduate or graduate courses.


Research mathematicians and graduate students.

Table of Contents

  • Preface to the English edition
  • Preface
  • Regular closed curves in the plane
  • \(C^r\) manifolds, \(C^r\) maps, and fiber bundles
  • Embeddings of \(C^\infty\) manifolds
  • Immersions of \(C^\infty\) manifolds
  • The Gromov convex integration theory
  • Foliations on open manifolds
  • Complex structures on open manifolds
  • Embeddings of \(C^\infty\) manifolds (continued)
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