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Hilbert's fifth problem and related topics

Author: Terence Tao
Publisher: Providence, Rhode Island : American Mathematical Society, [2014]
Series: Graduate studies in mathematics, v. 153.
Edition/Format:   Print book : Biography : EnglishView all editions and formats
Database:WorldCat
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Named Person: David Hilbert; David Hilbert; David Hilbert
Material Type: Biography
Document Type: Book
All Authors / Contributors: Terence Tao
ISBN: 9781470415648 147041564X
OCLC Number: 873238182
Description: xiii, 338 pages ; 27 cm.
Contents: Introduction --
Lie groups, Lie algebras, and the Baker-Campbell-Hausdorff formula --
Building Lie structure from representations and metrics --
Haar measure, the Peter-Weyl theorem, and compact or abelian groups --
Building metrics on groups, and the Gleason-Yamabe theorem --
The structure of locally compact groups --
Ultraproducts as a bridge between hard analysis and soft analysis --
Models of ultra approximate groups --
The microscopic structure of approximate groups --
Applications of the structural theory of approximate groups --
The Jordan-Schur theorem --
Nilpotent groups and nilprogressions --
Ado's theorem --
Associativity of the Baker-Campbell-Hausdorff-Dynkin law --
Local groups --
Central extensions of Lie groups, and cocycle averaging --
The Hilbert-Smith conjecture --
The Peter-Weyl theorem and nonabelian Fourier analysis --
Polynomial bounds via nonstandard analysis --
Loeb measure and the triangle removal lemma --
Two notes on Lie groups.
Series Title: Graduate studies in mathematics, v. 153.
Responsibility: Terence Tao.

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