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.
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Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
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ISBN-13
978-0-8218-4612-4 (9780821846124)
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Schweitzer Klassifikation
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).
