Hilbert s Fifth Problem and Related Topics is popular PDF and ePub book, written by Terence Tao in 2014-07-18, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Hilbert s Fifth Problem and Related Topics can be Read Online from any device for your convenience.
Hilbert s Fifth Problem and Related Topics Book PDF Summary
In the fifth of his famous list of 23 problems, Hilbert asked if every topological group which was locally Euclidean was in fact a Lie group. Through the work of Gleason, Montgomery-Zippin, Yamabe, and others, this question was solved affirmatively; more generally, a satisfactory description of the (mesoscopic) structure of locally compact groups was established. Subsequently, this structure theory was used to prove Gromov's theorem on groups of polynomial growth, and more recently in the work of Hrushovski, Breuillard, Green, and the author on the structure of approximate groups. In this graduate text, all of this material is presented in a unified manner, starting with the analytic structural theory of real Lie groups and Lie algebras (emphasising the role of one-parameter groups and the Baker-Campbell-Hausdorff formula), then presenting a proof of the Gleason-Yamabe structure theorem for locally compact groups (emphasising the role of Gleason metrics), from which the solution to Hilbert's fifth problem follows as a corollary. After reviewing some model-theoretic preliminaries (most notably the theory of ultraproducts), the combinatorial applications of the Gleason-Yamabe theorem to approximate groups and groups of polynomial growth are then given. A large number of relevant exercises and other supplementary material are also provided.
Detail Book of Hilbert s Fifth Problem and Related Topics PDF
- Author : Terence Tao
- Release : 18 July 2014
- Publisher : American Mathematical Soc.
- ISBN : 9781470415648
- Genre : Mathematics
- Total Page : 354 pages
- Language : English
- PDF File Size : 12,6 Mb
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