Hilbert's fifth problem and related topics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2014
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| Schriftenreihe: | Graduate studies in mathematics
153 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIII, 338 S. graph. Darst. |
| ISBN: | 9781470415648 |
Internformat
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| 490 | 1 | |a Graduate studies in mathematics |v 153 | |
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Datensatz im Suchindex
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| adam_text | Titel: Hilbert s fifth problem and related topics
Autor: Tao, Terence
Jahr: 2014
Contents Preface xi Notation xii Acknowledgments xiii Part 1. Hilbert’s Fifth Problem Chapter 1. Introduction 3 §1.1. Hilbert’s fifth problem 7 §1.2. Approximate groups 14 §1.3. Gromov’s theorem 20 Chapter 2. Lie groups, Lie algebras, and the Baker-Campbell- Hausdorff formula 25 §2.1. Local groups 26 §2.2. Some differential geometry 30 §2.3. The Lie algebra of a Lie group 34 §2.4. The exponential map 35 §2.5. The Baker-Campbell-Hausdorff formula 43 Chapter 3. Building Lie structure from representations and metrics 53 §3.1. The theorems of Cartan and von Neumann 57 §3.2. Locally compact vector spaces 60 §3.3. From Gleason metrics to Lie groups 64 Chapter 4. Haar measure, the Peter-Weyl theorem, and compact or abelian groups 73 vii
Contents viii §4.1. Haar measure 76 §4.2. The Peter-Weyl theorem 87 §4.3. The structure of locally compact abelian groups 94 Chapter 5. Building metrics on groups, and the Gleason-Yamabe theorem 99 §5.1. Warmup: the Birkhoff-Kakutani theorem 101 §5.2. Obtaining the commutator estimate via convolution 103 §5.3. Building metrics on NSS groups 106 §5.4. NSS from subgroup trapping 112 §5.5. The subgroup trapping property 114 §5.6. The local group case 117 Chapter 6. The structure of locally compact groups 125 §6.1. Van Dantzig’s theorem 127 §6.2. The invariance of domain theorem 131 §6.3. Hilbert’s fifth problem 133 §6.4. Transitive actions 136 Chapter 7. Ultraproducts as a bridge between hard analysis and soft analysis §7.1. Ultrafilters §7.2. Ultrapowers and ultralimits §7.3. Nonstandard finite sets and nonstandard finite sums §7.4. Asymptotic notation §7.5. Ultra approximate groups Chapter 8. Models of ultra approximate groups §8.1. Ultralimits of metric spaces (Optional) §8.2. Sanders-Croot-Sisask theory §8.3. Locally compact models of ultra approximate groups §8.4. Lie models of ultra approximate groups Chapter 9. The microscopic structure of approximate groups §9.1. Gleason’s lemma §9.2. A cheap version of the structure theorem §9.3. Local groups 139 144 148 157 158 161 167 169 176 184 190 197 204 208 212 Chapter 10. Applications of the structural theory of approximate groups 219
Contents ix §10.1. Sets of bounded doubling 220 §10.2. Polynomial growth 223 §10.3. Fundamental groups of compact manifolds (optional) 225 §10.4. A Margulis-type lemma 229 Part 2. Related Articles Chapter 11. The Jordan-Schur theorem 233 §11.1. Proofs 234 Chapter 12. Nilpotent groups and nilprogressions 237 §12.1. Some elementary group theory 239 §12.2. Nilprogressions 244 Chapter 13. Ado’s theorem 249 §13.1. The nilpotent case 252 §13.2. The solvable case 254 §13.3. The general case 258 Chapter 14. Associativity of the Baker-Campbell-Hausdorff-Dynkin law 259 Chapter 15. Local groups 265 §15.1. Lie’s third theorem 269 §15.2. Globalising a local group 270 §15.3. A nonglobalisable group 274 Chapter 16. Central extensions of Lie groups, and cocycle averaging 277 §16.1. A little group cohomology 279 §16.2. Proof of theorem 285 Chapter 17. The Hilbert-Smith conjecture 289 §17.1. Periodic actions of prime order 290 §17.2. Reduction to the p-adic case 293 Chapter 18. The Peter-Weyl theorem and nonabelian Fourier analysis 297 §18.1. Proof of the Peter-Weyl theorem 298 §18.2. Nonabelian Fourier analysis 302 Chapter 19. Polynomial bounds via nonstandard analysis 307 Chapter 20. Loeb measure and the triangle removal lemma 313
X Contents §20.1. Loeb measure 316 §20.2. The triangle removal lemma 321 Chapter 21. Two notes on Lie groups 325 Bibliography 329 Index 335
|
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| indexdate | 2024-07-10T01:13:34Z |
| institution | BVB |
| isbn | 9781470415648 |
| language | English |
| lccn | 2014009022 |
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| oclc_num | 889991773 |
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| spelling | Tao, Terence 1975- Verfasser (DE-588)132190370 aut Hilbert's fifth problem and related topics Terence Tao Providence, RI American Mathematical Society 2014 XIII, 338 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 153 Includes bibliographical references and index Hilbert, David 1862-1943 Lie-Algebra (DE-588)4130355-6 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Lie groups Lie algebras Characteristic functions Lie-Gruppe (DE-588)4035695-4 s Lie-Algebra (DE-588)4130355-6 s DE-604 Graduate studies in mathematics 153 (DE-604)BV009739289 153 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027575756&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tao, Terence 1975- Hilbert's fifth problem and related topics Graduate studies in mathematics Hilbert, David 1862-1943 Lie-Algebra (DE-588)4130355-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| subject_GND | (DE-588)4130355-6 (DE-588)4035695-4 |
| title | Hilbert's fifth problem and related topics |
| title_auth | Hilbert's fifth problem and related topics |
| title_exact_search | Hilbert's fifth problem and related topics |
| title_full | Hilbert's fifth problem and related topics Terence Tao |
| title_fullStr | Hilbert's fifth problem and related topics Terence Tao |
| title_full_unstemmed | Hilbert's fifth problem and related topics Terence Tao |
| title_short | Hilbert's fifth problem and related topics |
| title_sort | hilbert s fifth problem and related topics |
| topic | Hilbert, David 1862-1943 Lie-Algebra (DE-588)4130355-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd |
| topic_facet | Hilbert, David 1862-1943 Lie-Algebra Lie-Gruppe |
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