TY  - BOOK
AU  - Tao,Terence
TI  - Hilbert's fifth problem and related topics
T2  - Graduate studies in mathematics
SN  - 9781470415648 (hbk : alk. paper)
U1  - 512.482 23
PY  - 2014///
CY  - Providence
PB  - American Mathematical Society
KW  - Lie groups
KW  - Lie algebras
KW  - Characteristic functions
N1  - Includes bibliographical references and index; 1. Introduction --
2. Lie groups, Lie algebras, and the Baker-Campbell-Hausdorff formula --
3. Building Lie structure from representations and metrics --
4. Haar measure, the Peter-Weyl theorem, and compact or abelian groups --
5. Building metrics on groups, and the Gleason-Yamabe theorem --
6. The structure of locally compact groups --
7. Ultraproducts as a bridge between hard analysis and soft analysis --
8. Models of ultra approximate groups --
9. The microscopic structure of approximate groups --
10. Applications of the structural theory of approximate groups --
11. The Jordan-Schur theorem --
12. Nilpotent groups and nilprogressions --
13. Ado's theorem --
14. Associativity of the Baker-Campbell-Hausdorff-Dynkin law --
15. Local groups --
16. Central extensions of Lie groups, and cocycle averaging --
17. The Hilbert-Smith conjecture --
18. The Peter-Weyl theorem and nonabelian Fourier analysis --
19. Polynomial bounds via nonstandard analysis --
20. Loeb measure and the triangle removal lemma --
21. Two notes on Lie groups--
Bibliography--
Index
ER  -