Embedding problems in symplectic geometry:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
<<de>> Gruyter
2005
|
| Series: | De Gruyter expositions in mathematics
40 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis Klappentext |
| Physical Description: | X, 250 S. Ill., graph. Darst. |
| ISBN: | 3110178761 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface vii
1 Introduction 1
1.1 From classical mechanics to symplectic geometry 1
1.2 Symplectic embedding obstructions 4
1.3 Symplectic embedding constructions 11
2 Proof of Theorem 1 23
2.1 Comparison of the relations </ 23
2.2 Rigidity for ellipsoids 24
2.3 Rigidity for polydiscs ? 28
3 Proof of Theorem 2 31
3.1 Reformulation of Theorem 2 31
3.2 The folding construction 39
3.3 End of fee proof 47
4 Multiple symplectic folding in four dimensions 52
4.1 Modification of fee folding construction 52
4.2 Multiple folding 53
4.3 Embeddings into balls 57
4.4 Embeddings into cubes 73
5 Symplectic folding in higher dimensions 82
5.1 Four types of folding 82
5.2 Embedding polydiscs into cubes 84
5.3 Embedding ellipsoids into balls 90
6 Proof of Theorem 3 107
6.1 Proof of lima_>oo p% (M, <y) = 1 107
6.2 Proof of limbec Pa (M, &>) = 1 123
6.3 Asymptotic embedding invariants 147
X Contents
7 Symplectic wrapping 149
7.1 The wrapping construction 149
7.2 Folding versus wrapping 157
8 Proof of Theorem 4 162
8.1 A more general statement 162
8.2 A further motivation for Problem f 165
8.3 Proof by symplectic folding 168
8.4 Proof by symplectic lifting 177
9 Packing symplectic manifolds by hand 188
9.1 Motivations for the symplectic packing problem 189
9.2 The packing numbers of the 4-ball and CP2 and of ruled symplectic
4-manifolds 194
9.3 Explicit maximal packings in four dimensions 198
9.4 Maximal packings in higher dimensions 213
Appendix 215
A The Extension after Restriction Principle 215
B Flexibility for volume preserving embeddings 219
C Symplectic capacities and the invariants eg and cq 224
D Computer programs 235
E Some other symplectic embedding problems 238
References 241
Index 247
lee tic geometry is the geometry junderlyiiig Hamiltonian dynamic^
;and symplectic mappings arise as (ime-l Jmapsof ]iam;i|tonia.n flows. T ~>^
Spectacular rigidity phenomena for symplectic mappings discovered in thw
■last two decades show,that certain things cannot be dorie; by a symplectic:
mapping. For instance, Gromov s famous ndtf squeezing theorem states-
that one carjnof map a ball into a .tjhinner cyljsnder.,,by a syqipiectic enn-
The aim of this book is to show that certain other things can be clone by
symplectic mappings. This is achieved by various elementary and explicit
symplectic embedding constructions, such as folding , wrapping and
IIMfting . These constructions are carried out in detail and are used to solve
*some specific symplectic embedding problems
:jThe exposition is self-contained and adliresse dio st uclents and researchers 5
interested in geometry or dvnamics.
|
| any_adam_object | 1 |
| author | Schlenk, Felix |
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| dewey-full | 516.3/6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/6 |
| dewey-search | 516.3/6 |
| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 3110178761 |
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| publishDate | 2005 |
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| spelling | Schlenk, Felix Verfasser aut Embedding problems in symplectic geometry by Felix Schlenk Berlin [u.a.] <<de>> Gruyter 2005 X, 250 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 40 Géométrie symplectique Plongements (Mathématiques) Embeddings (Mathematics) Symplectic geometry Einbettung Mathematik (DE-588)4151233-9 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 gnd rswk-swf Symplektische Geometrie (DE-588)4194232-2 s Einbettung Mathematik (DE-588)4151233-9 s DE-604 De Gruyter expositions in mathematics 40 (DE-604)BV004069300 40 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2603890&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UBPassau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013186404&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013186404&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Schlenk, Felix Embedding problems in symplectic geometry De Gruyter expositions in mathematics Géométrie symplectique Plongements (Mathématiques) Embeddings (Mathematics) Symplectic geometry Einbettung Mathematik (DE-588)4151233-9 gnd Symplektische Geometrie (DE-588)4194232-2 gnd |
| subject_GND | (DE-588)4151233-9 (DE-588)4194232-2 |
| title | Embedding problems in symplectic geometry |
| title_auth | Embedding problems in symplectic geometry |
| title_exact_search | Embedding problems in symplectic geometry |
| title_full | Embedding problems in symplectic geometry by Felix Schlenk |
| title_fullStr | Embedding problems in symplectic geometry by Felix Schlenk |
| title_full_unstemmed | Embedding problems in symplectic geometry by Felix Schlenk |
| title_short | Embedding problems in symplectic geometry |
| title_sort | embedding problems in symplectic geometry |
| topic | Géométrie symplectique Plongements (Mathématiques) Embeddings (Mathematics) Symplectic geometry Einbettung Mathematik (DE-588)4151233-9 gnd Symplektische Geometrie (DE-588)4194232-2 gnd |
| topic_facet | Géométrie symplectique Plongements (Mathématiques) Embeddings (Mathematics) Symplectic geometry Einbettung Mathematik Symplektische Geometrie |
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