Embeddings and Immersions

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

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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
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