Morse homology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel u.a.
Birkhäuser
1993
|
| Series: | Progress in mathematics
111 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 235 S. graph. Darst. |
| ISBN: | 3764329041 0817629041 |
Staff View
MARC
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| 490 | 1 | |a Progress in mathematics |v 111 | |
| 650 | 4 | |a Teoría de Morse | |
| 650 | 4 | |a Teoría homológica | |
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Record in the Search Index
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| adam_text | Contents
List of symbols viii
1 Introduction
1.1 Background 1
1.1.1 Classical Morse Theory 1
1.1.2 Relative Morse Theory 5
1.1.3 The Continuation Principle 7
1.2 Overview 8
1.2.1 The Construction of the Morse Homology 8
1.2.2 The Axiomatic Approach 10
1.3 Remarks on the Methods 14
1.4 Table of Contents 17
1.5 Acknowledgments 18
2 The Trajectory Spaces
2.1 The Construction of the Trajectory Spaces 21
2.2 Predholm Theory 29
2.2.1 The Fredholm Operator on the Trivial Bundle 29
2.2.2 The Fredholm Operator on Non Trivial Bundles .... 39
2.2.3 Generalization to Fredholm Maps 41
2.3 Transversality 41
2.3.1 The Regularity Conditions 42
2.3.2 The Regularity Results 49
vi CONTENTS
2.4 Compactness 51
2.4.1 The Space of Unparametrized Trajectories 52
2.4.2 The Compactness Result for Unparametrized Trajectories 55
2.4.3 The Compactness Result for Homotopy Trajectories . . 63
2.4.4 The Compactness Result for A Parametrized Trajectories 67
2.5 Gluing 68
2.5.1 Gluing for the Time Independent Trajectory Spaces . . 68
2.5.2 Gluing of Trajectories of the Time Dependent Gradient
Flow 96
2.5.3 Gluing for A Parametrized Trajectories 99
3 Orientation
3.1 Orientation and Gluing in the Trivial Case 104
3.1.1 The Determinant Bundle 104
3.1.2 Gluing and Orientation for Fredholm Operators 107
3.2 Coherent Orientation 113
3.2.1 Orientation and Gluing on the Manifold M 115
4 Morse Homology Theory
4.1 The Main Theorems of Morse Homology 133
4.1.1 Canonical Orientations 133
4.1.2 The Morse Complex 135
4.1.3 The Canonical Isomorphism 140
4.1.4 Topology and Coherent Orientation 153
4.2 The Eilenberg Steenrod Axioms 163
4.2.1 Extension of Morse Functions and Induced Morse Func¬
tions on Vector Bundles 164
4.2.2 The Homology Functor and Homotopy In variance ... 169
4.2.3 Relative Morse Homology 180
4.2.4 Summary 193
4.3 The Uniqueness Result 194
CONTENTS vii
5 Extensions
5.1 Morse Cohomology 199
5.2 Poincare Duality 200
5.3 Products 202
A Curve Spaces and Banach Bundles
A.I The Manifold of Maps V*%(R,M) 207
A.2 Banach Bundles on V*%(R,M) 214
B The Geometric Boundary Operator 221
Bibliography 229
Index 232
|
| any_adam_object | 1 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.23 |
| dewey-search | 514.23 |
| dewey-sort | 3514.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:08:48Z |
| institution | BVB |
| isbn | 3764329041 0817629041 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005093365 |
| oclc_num | 318380174 |
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| physical | IX, 235 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Schwarz, Matthias Verfasser aut Morse homology Matthias Schwarz Basel u.a. Birkhäuser 1993 IX, 235 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 111 Teoría de Morse Teoría homológica Homologie (DE-588)4141951-0 gnd rswk-swf Morse-Theorie (DE-588)4197103-6 gnd rswk-swf Morse-Theorie (DE-588)4197103-6 s Homologie (DE-588)4141951-0 s DE-604 Progress in mathematics 111 (DE-604)BV000004120 111 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005093365&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schwarz, Matthias Morse homology Progress in mathematics Teoría de Morse Teoría homológica Homologie (DE-588)4141951-0 gnd Morse-Theorie (DE-588)4197103-6 gnd |
| subject_GND | (DE-588)4141951-0 (DE-588)4197103-6 |
| title | Morse homology |
| title_auth | Morse homology |
| title_exact_search | Morse homology |
| title_full | Morse homology Matthias Schwarz |
| title_fullStr | Morse homology Matthias Schwarz |
| title_full_unstemmed | Morse homology Matthias Schwarz |
| title_short | Morse homology |
| title_sort | morse homology |
| topic | Teoría de Morse Teoría homológica Homologie (DE-588)4141951-0 gnd Morse-Theorie (DE-588)4197103-6 gnd |
| topic_facet | Teoría de Morse Teoría homológica Homologie Morse-Theorie |
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