Differential algebraic topology: from stratifolds to exotic spheres
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2010
|
| Series: | Graduate studies in mathematics
vol. 110 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 218 S. graph. Darst. |
| ISBN: | 9780821848982 |
Staff View
MARC
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| 100 | 1 | |a Kreck, Matthias |d 1947- |e Verfasser |0 (DE-588)108556077 |4 aut | |
| 245 | 1 | 0 | |a Differential algebraic topology |b from stratifolds to exotic spheres |c Matthias Kreck |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2010 | |
| 300 | |a XII, 218 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate studies in mathematics |v vol. 110 | |
| 650 | 4 | |a Algebraic topology | |
| 650 | 4 | |a Differential topology | |
| 650 | 0 | 7 | |a Differentialtopologie |0 (DE-588)4012255-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Topologie |0 (DE-588)4120861-4 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Differentialtopologie |0 (DE-588)4012255-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-1592-1 |
| 830 | 0 | |a Graduate studies in mathematics |v vol. 110 |w (DE-604)BV009739289 |9 110 | |
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Record in the Search Index
| _version_ | 1804140788406288384 |
|---|---|
| adam_text | Contents
INTRODUCTION
ix
Chapter
0.
A quick introduction to stratifolds
1
Chapter
1.
Smooth manifolds revisited
5
§1.
A word about structures
5
§2.
Differential spaces
6
§3.
Smooth manifolds revisited
8
§4.
Exercises
11
Chapter
2.
Stratifolds
15
§1.
Stratifolds
15
§2.
Local retractions
18
§3.
Examples
19
§4.
Properties of smooth maps
25
§5.
Consequences of Sard s Theorem
27
§6.
Exercises
29
Chapter
3.
Stratifolds with boundary: c-stratifolds
33
§1.
Exercises
38
Chapter
4.
Z/2-homology
39
§1.
Motivation of homology
39
§2.
Z/2-oriented stratifolds
41
§3.
Regular stratifolds
43
§4.
Z/2-homołogy
45
vi
Contents
§5.
Exercises
51
Chapter
5.
The Mayer-Vietoris sequence and homology groups of
spheres
55
§1.
The Mayer-Vietoris sequence
55
§2.
Reduced homology groups and homology groups of spheres
61
§3.
Exercises
64
Chapter
6.
Brouwer s fixed point theorem, separation,
invariance
of
dimension
67
§1.
Brouwer s fixed point theorem
67
§2.
A separation theorem
68
§3.
Invariance
of dimension
69
§4.
Exercises
70
Chapter
7.
Homology of some important spaces and the
Euler
characteristic
71
§1.
The fundamental class
71
§2.
Z/2-homology of
projective
spaces
72
§3.
Betti
numbers and the
Euler
characteristic
74
§4.
Exercises
77
Chapter
8.
Integral homology and the mapping degree
79
§1.
Integral homology groups
79
§2.
The degree
83
§3.
Integral homology groups of
projective
spaces
86
§4.
A comparison between integral and Z/2-homology
88
§5.
Exercises
89
Chapter
9.
A comparison theorem for homology theories and
CW-complexes
93
§1.
The axioms of a homology theory
93
§2.
Comparison of homology theories
94
§3.
CW-complexes
98
§4.
Exercises
99
Chapter
10.
Künneth s
theorem
103
§1.
The cross product
103
§2.
The Kiinneth theorem
106
S3.
Exercises
109
Contents
vii
Chapter
11.
Some lens spaces and quaternionic generalizations 111
§1.
Lens spaces 111
§2.
Milnor s 7-dimensional manifolds
115
§3.
Exercises
117
Chapter
12.
Cohomology and
Poincaré
duality
119
§1.
Cohomology groups
119
§2.
Poincaré
duality
121
§3.
The Mayer-Vietoris sequence
123
§4.
Exercises
125
Chapter
13.
Induced maps and the cohomology axioms
127
§1.
Transversality for stratifolds
127
§2.
The induced maps
129
§3.
The cohomology axioms
132
§4.
Exercises
133
Chapter
14.
Products in cohomology and the
Kronecker
pairing
135
§1.
The cross product and the
Künneth
theorem
135
§2.
The cup product
137
§3.
The
Kronecker
pairing
141
§4.
Exercises
145
Chapter
15.
The signature
147
§1.
Exercises
152
Chapter
16.
The
Euler
class
153
§1.
The
Euler
class
153
§2.
Euler
classes of some bundles
155
§3.
The top
Stiefel-
Whitney class
159
§4.
Exercises
159
Chapter
17.
Chern classes and
Stiefel-
Whitney classes
161
§1.
Exercises
165
Chapter
18.
Pontrjagin classes and applications to bordism
167
§1.
Pontrjagin classes
167
§2.
Pontrjagin numbers
170
§3.
Applications of Pontrjagin numbers to bordism
172
§4.
Classification of some Milnor manifolds
174
viii Contents
§5.
Exercises
175
Chapter
19.
Exotic 7-spheres
177
§1.
The signature theorem and exotic 7-spheres
177
§2.
The Milnor spheres are homeomorphic to the 7-sphere
181
§3.
Exercises
184
Chapter
20.
Relation to ordinary singular (co)homology
185
§1.
SHk(X) is isomorphic to
Нк{Х Ћ)
for CVF-complexes
185
§2.
An example where SHk(X) and
Н)~(Х)
are different
187
§3.
SHk(M) is isomorphic to ordinary singular cohomology
188
§4.
Exercises
190
Appendix A. Constructions of stratifolds
191
§1.
The product of two stratifolds
191
§2.
Gluing along part of the boundary
192
§3.
Proof of Proposition
4.1 194
Appendix B. The detailed proof of the Mayer-Vietoris sequence
197
Appendix C. The tensor product
209
Bibliography
215
Index
217
|
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| ctrlnum | (OCoLC)444109034 (DE-599)BVBBV035827807 |
| dewey-full | 514/.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.2 |
| dewey-search | 514/.2 |
| dewey-sort | 3514 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| spelling | Kreck, Matthias 1947- Verfasser (DE-588)108556077 aut Differential algebraic topology from stratifolds to exotic spheres Matthias Kreck Providence, RI American Math. Soc. 2010 XII, 218 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics vol. 110 Algebraic topology Differential topology Differentialtopologie (DE-588)4012255-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Algebraische Topologie (DE-588)4120861-4 s Differentialtopologie (DE-588)4012255-4 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1592-1 Graduate studies in mathematics vol. 110 (DE-604)BV009739289 110 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018686410&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kreck, Matthias 1947- Differential algebraic topology from stratifolds to exotic spheres Graduate studies in mathematics Algebraic topology Differential topology Differentialtopologie (DE-588)4012255-4 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| subject_GND | (DE-588)4012255-4 (DE-588)4120861-4 |
| title | Differential algebraic topology from stratifolds to exotic spheres |
| title_auth | Differential algebraic topology from stratifolds to exotic spheres |
| title_exact_search | Differential algebraic topology from stratifolds to exotic spheres |
| title_full | Differential algebraic topology from stratifolds to exotic spheres Matthias Kreck |
| title_fullStr | Differential algebraic topology from stratifolds to exotic spheres Matthias Kreck |
| title_full_unstemmed | Differential algebraic topology from stratifolds to exotic spheres Matthias Kreck |
| title_short | Differential algebraic topology |
| title_sort | differential algebraic topology from stratifolds to exotic spheres |
| title_sub | from stratifolds to exotic spheres |
| topic | Algebraic topology Differential topology Differentialtopologie (DE-588)4012255-4 gnd Algebraische Topologie (DE-588)4120861-4 gnd |
| topic_facet | Algebraic topology Differential topology Differentialtopologie Algebraische Topologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018686410&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009739289 |
| work_keys_str_mv | AT kreckmatthias differentialalgebraictopologyfromstratifoldstoexoticspheres |