An introduction to Morse theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Japanese |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2002
|
| Schriftenreihe: | Translations of mathematical monographs
208 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Japan. übers. Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIV, 219 S. graph. Darst. |
| ISBN: | 0821810227 9780821810224 |
Internformat
MARC
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| 240 | 1 | 0 | |a Morse riron no kiso |
| 245 | 1 | 0 | |a An introduction to Morse theory |c Yukio Matsumoto |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2002 | |
| 300 | |a XIV, 219 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 1 | |a Translations of mathematical monographs |v 208 | |
| 490 | 0 | |a Iwanami series in modern mathematics | |
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| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
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| 650 | 0 | 7 | |a Morse-Theorie |0 (DE-588)4197103-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804128033539358720 |
|---|---|
| adam_text | Contents
Preface ix
Preface to the English Translation xi
Objectives xiii
Chapter 1. Morse Theory on Surfaces 1
1.1. Critical points of functions 1
1.2. Hessian 3
1.3. The Morse lemma 8
1.4. Morse functions on surfaces 14
1.5. Handle decomposition 22
a. The case when the index of j?o is zero 26
b. The case when the index of p0 is one 26
c. The case when the index of po is two 29
d. Handle decompositions 30
Summary 31
Exercises 31
Chapter 2. Extension to General Dimensions 33
2.1. Manifolds of dimension m 33
a. Functions on a manifold and maps between mani¬
folds 33
b. Manifolds with boundary 34
c. Functions and maps on manifolds with boundary 38
2.2. Morse functions 41
a. Morse functions on m manifolds 41
b. The Morse lemma for dimension m 44
c. Existence of Morse functions 47
2.3. Gradient like vector fields 56
a. Tangent vectors 56
vi CONTENTS
b. Vector fields 61
c. Gradient like vector fields 63
2.4. Raising and lowering critical points 69
Summary 71
Exercises 71
Chapter 3. Handlebodies 73
3.1. Handle decompositions of manifolds 73
3.2. Examples 83
3.3. Sliding handles 105
3.4. Canceling handles 120
Summary 130
Exercises 131
Chapter 4. Homology of Manifolds 133
4.1. Homology groups 133
4.2. Morse inequality 141
a. Handlebodies and cell complexes 141 ¦
b. Proof of the Morse inequality 147
c. Homology groups of complex projective space
CPm 147
4.3. Poincare duality 148
a. Cohomology groups 148
b. Proof of Poincare duality 150
4.4. Intersection forms 158
a. Intersection numbers of submanifolds 159
b. Intersection forms 159
c. Intersection numbers of submanifolds and inter¬
section forms 163
Summary 164
Exercises 164
Chapter 5. Low dimensional Manifolds 167
5.1. Fundamental groups 167
5.2. Closed surfaces and 3 dimensional manifolds 173
a. Closed surfaces 173
b. 3 dimensional manifolds 181
5.3. 4 dimensional manifolds 186
a. Heegaard diagrams for 4 dimensional manifolds 186
b. The case N = D4 190
c. Kirby calculus 194
CONTENTS vii
Summary 197
Exercises 197
A View from Current Mathematics 199
Answers to Exercises 203
Bibliography 213
Recommended Reading 215
Index 217
|
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| dewey-ones | 514 - Topology |
| dewey-raw | 514 |
| dewey-search | 514 |
| dewey-sort | 3514 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV013267445 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:42:49Z |
| institution | BVB |
| isbn | 0821810227 9780821810224 |
| language | English Japanese |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009045132 |
| oclc_num | 248499475 |
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| physical | XIV, 219 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Translations of mathematical monographs |
| series2 | Translations of mathematical monographs Iwanami series in modern mathematics |
| spelling | Matsumoto, Yukio 1944- Verfasser (DE-588)136960693 aut Morse riron no kiso An introduction to Morse theory Yukio Matsumoto Providence, RI American Math. Soc. 2002 XIV, 219 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Translations of mathematical monographs 208 Iwanami series in modern mathematics Aus dem Japan. übers. Hier auch später erschienene, unveränderte Nachdrucke Morse-Theorie Morse-Theorie (DE-588)4197103-6 gnd rswk-swf Morse-Theorie (DE-588)4197103-6 s DE-604 Translations of mathematical monographs 208 (DE-604)BV000002394 208 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009045132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Matsumoto, Yukio 1944- An introduction to Morse theory Translations of mathematical monographs Morse-Theorie Morse-Theorie (DE-588)4197103-6 gnd |
| subject_GND | (DE-588)4197103-6 |
| title | An introduction to Morse theory |
| title_alt | Morse riron no kiso |
| title_auth | An introduction to Morse theory |
| title_exact_search | An introduction to Morse theory |
| title_full | An introduction to Morse theory Yukio Matsumoto |
| title_fullStr | An introduction to Morse theory Yukio Matsumoto |
| title_full_unstemmed | An introduction to Morse theory Yukio Matsumoto |
| title_short | An introduction to Morse theory |
| title_sort | an introduction to morse theory |
| topic | Morse-Theorie Morse-Theorie (DE-588)4197103-6 gnd |
| topic_facet | Morse-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009045132&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000002394 |
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