Symplectic geometry: an introduction based on the seminar in Bern, 1992
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Basel u.a.
Birkhäuser
1994
|
| Series: | Progress in mathematics
124 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 239 S. graph. Darst. |
| ISBN: | 3764350644 0817650644 |
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MARC
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| 245 | 1 | 0 | |a Symplectic geometry |b an introduction based on the seminar in Bern, 1992 |c B. Aebischer ... |
| 264 | 1 | |a Basel u.a. |b Birkhäuser |c 1994 | |
| 300 | |a XII, 239 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 124 | |
| 650 | 0 | 7 | |a Symplektische Geometrie |0 (DE-588)4194232-2 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 1992 |z Bern |2 gnd-content | |
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| 700 | 1 | |a Aebischer, Beat |e Sonstige |4 oth | |
| 830 | 0 | |a Progress in mathematics |v 124 |w (DE-604)BV000004120 |9 124 | |
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Record in the Search Index
| _version_ | 1804123960592302080 |
|---|---|
| adam_text | Contents
Preface
....................................
¡x
1
Introduction
1.1
Symplectic
Linear Algebra
..................... 1
1.2
Symplectic
Manifolds
........................ 2
1.3
Hamiltonian Systems
........................ 4
1.4
The Maslov Index
......................... 7
2
Darboux
Theorem and Examples of
Symplectic
Manifolds
2.1
The Theorem of
Darboux
..................... 17
2.2
The Cotangent Bundle
....................... 22
2.3 Kahler
Manifolds
.......................... 23
2.4
Coadjoint Orbits
.......................... 32
2.5
An Example: CPn as a Symplectic Manifold
.......... 40
3
Generating Functions
3.1
Minimax
Principie
and
Lustemik-Schnirełman
Theory
..... 43
3.2 Lagrange submanifolds....................... 48
3.3
Generating functions
........................ 49
3.4
The action functional considered as a generating function
... 52
3.5
Critical points for generating functions
.............. 56
3.6
Stabilization
............................. 59
3.7
Symplectic diffeomorphisms of R2n
................ 60
3.8
The Viterbo capacities
....................... 63
4
Symplectic Capacities
4.1
Existence of Periodic Solutions
.................. 65
4.2
Symplectic Capacities
....................... 73
5
Ploer Homology
5.1
Morse Homology and the Coniey Index
.............. 79
5.2
The Arnoi d Conjecture
...................... 86
5.3
The Variational Setup
....................... 88
5.4
Definition of
Floer
Homology
................... 91
5.5
Continuation of
Floer
Homology
................. 93
5.6
Floer
Homology Equals Singular Homology
........... 95
5.7
Symplectic Homology
....................... 97
Contents
Pseudoholomorphic
Curves
6.1
Introduction
............................. 99
6.1.1 Lineax
algebra
of symplectic and almost
complex structures
..................... 99
6.1.2
Definition of pseudoholomorphic curves
......... 102
6.1.3
Regularity of holomorphic curves
............. 103
6.2
The Moduli Space of Holomorphic Curves
............ 104
6.2.1
The setting of global analysis
............... 104
6.2.2
The operator Bj and its linearization
........... 109
6.2.3
The moduli space at regular almost complex
structures
.......................... 114
6.2.4
Comparison of moduli spaces at different complex
structures
.......................... 119
6.3
Compactness of the Moduli Space
................ 119
6.3.1
A homological criterion for injectivity
.......... 120
6.3.2
An
apriori
inequality
.................... 126
6.3.3
Weak compactness
..................... 135
6.3.4
Removing singularities
................... 138
6.3.5
A compactness and an existence result
.......... 142
6.3.6
An application
....................... 145
7
Gromov s Compactness Theorem from a Geometrical
Point of View
7.1
Gromov-Schwarz Lemma,
Monotonicity,
Removing
Singularities
............................. 147
7.2
Deformation of Surfaces and Convergence of Hyperbolic
Structures
.............................. 150
7.3
Gromov s Compactness Theorem
................. 155
8
Contact structures
8.1
Contact manifolds
......................... 167
8.2
Symplectification
.......................... 173
8.3
Strictly pseudoconvex surfaces
.................. 178
8.4
Contact structures on 3-manifolds
................ 182
8.4.1
Plane fields on 3-manifolds
................ 182
8.4.2
Invariant contact structures on the solid torus
...... 184
8.4.3
Martinet s theorem
..................... 188
Contents
vii
8.5
Two-dimensional surfaces in contact manifolds
......... 190
8.5.1
Germs of contact structures on 2-dimensional
surfaces
........................... 190
8.5.2
Invariants for curves in contact manifolds
........ 195
8.5.3
Index theorems for 2-dimensional surfaces
........ 199
8.5.4
Bennequin s inequality
................... 205
8.6
Holomorphic filling
......................... 206
8.6.1
Bishop s theorem
...................... 206
8.6.2
One-parameter families of holomorphic discs
...... 210
8.6.3
Fillable contact structures
................. 213
8.7
Eliashberg s classification of 3-dimensional contact
structures
..............,................ 217
A Generalities on Homology and Cohomology
A.I Axioms for homology
........................ 220
A.2 Axioms for cohomology
...................... 221
A.3 Homomorphisms of (co)homology sequences
........... 222
A.4 The (cojhomology sequence of a triple
.............. 222
A.
5
Homotopy equivalence and contractibility
............ 224
A.6 Direct sums
............................. 225
A.7 Triads
................................ 225
A.
8
Mayer-Vietoris sequence of a triad
................ 226
References
.................................. 229
Index
..................................... 237
|
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| genre_facet | Konferenzschrift 1992 Bern |
| id | DE-604.BV009620298 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:38:04Z |
| institution | BVB |
| isbn | 3764350644 0817650644 |
| language | English |
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| physical | XII, 239 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
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| publisher | Birkhäuser |
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| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Symplectic geometry an introduction based on the seminar in Bern, 1992 B. Aebischer ... Basel u.a. Birkhäuser 1994 XII, 239 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 124 Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1992 Bern gnd-content Symplektische Geometrie (DE-588)4194232-2 s DE-604 Aebischer, Beat Sonstige oth Progress in mathematics 124 (DE-604)BV000004120 124 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006358282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Symplectic geometry an introduction based on the seminar in Bern, 1992 Progress in mathematics Symplektische Geometrie (DE-588)4194232-2 gnd |
| subject_GND | (DE-588)4194232-2 (DE-588)1071861417 |
| title | Symplectic geometry an introduction based on the seminar in Bern, 1992 |
| title_auth | Symplectic geometry an introduction based on the seminar in Bern, 1992 |
| title_exact_search | Symplectic geometry an introduction based on the seminar in Bern, 1992 |
| title_full | Symplectic geometry an introduction based on the seminar in Bern, 1992 B. Aebischer ... |
| title_fullStr | Symplectic geometry an introduction based on the seminar in Bern, 1992 B. Aebischer ... |
| title_full_unstemmed | Symplectic geometry an introduction based on the seminar in Bern, 1992 B. Aebischer ... |
| title_short | Symplectic geometry |
| title_sort | symplectic geometry an introduction based on the seminar in bern 1992 |
| title_sub | an introduction based on the seminar in Bern, 1992 |
| topic | Symplektische Geometrie (DE-588)4194232-2 gnd |
| topic_facet | Symplektische Geometrie Konferenzschrift 1992 Bern |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006358282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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