Embeddings and immersions
Author(s)
Bibliographic Information
Embeddings and immersions
（Translations of mathematical monographs, v. 124）
American Mathematical Society, c1993
- : soft cover
- Other Title
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埋め込みとはめ込み
Umekomi to hamekomi
Available at / 44 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
ADA||15||1(H)93025787
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc20:516.3/ad112070260153
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
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.
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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