Embeddings and Immersions

American Mathematical Soc., 1993 - Mathematics - 183 pages
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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Contents

 III 1 IV 7 V 15 VI 32 VII 37 VIII 42 IX 45 X 47
 XXX 108 XXXI 111 XXXII 114 XXXIII 116 XXXIV 123 XXXV 127 XXXVI 128 XXXVIII 129

 XI 49 XII 53 XIII 57 XIV 60 XV 62 XVI 65 XVII 66 XVIII 75 XIX 76 XX 79 XXI 85 XXII 86 XXIII 89 XXIV 91 XXV 92 XXVI 93 XXVII 94 XXVIII 95 XXIX 97
 XL 131 XLI 134 XLII 135 XLIII 136 XLIV 137 XLV 141 XLVI 142 XLVII 146 XLVIII 150 XLIX 155 L 157 LI 160 LII 163 LIII 167 LIV 177 LV 179 LVI 181 Copyright