Hilbert’s fifth problem and related topics.
Terence TaoIn preparation
Last updated:Dec 14, 2012
This continues my series of books derived from my blog, and is based on the lecture notes for my graduate course of the same name. The preceding books in this series were “Structure and Randomness“, “Poincaré’s legacies“, “An epsilon of room“, “An introduction to measure theory“, “Topics in random matrix theory“, “Higher order Fourier analysis“, and “Compactness and contradiction“.
A draft version of the MS can be found here.
Pre-errata (to be corrected in the published version):
- Page 20: In Problem 1.1.14, the hypothesis that G has polynomial growth is missing and should be inserted.
- Page 79: In the last paragraph, a right parenthesis is missing after “Exercise 1.4.3″.
Thanks to Michael Cowling for corrections.
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27 March, 2012 at 11:00 am
Hilbert’s fifth problem and related topics « What’s new
[...] finished the first draft of the the first of my books based on my 2011 blog posts, entitled “Hilbert’s fifth problem and related topics“, based on the lecture notes for my graduate course of the same name. The PDF of this draft [...]
29 March, 2012 at 11:54 pm
Mads Sørensen
Typographical suggestions:
P. 5, l. 5 in the proof:
‘s in 
shouldn’t be in italic mode.
The
P. 6, l. 2 in exercise 1.1.4:
‘s in 
shouldn’t be in italic mode.
The
P. 8, l. 1 after the two times two matrix:
‘s in 
supposed to be in italic mode?
Is the
P. 17, footnote 4:
Use \dots instead of “…” and remember a comma after the definition of the group G_{3}.
In general:
When typing a map, use \colon instead of a normal colon. (The spacing is incorrect.) Also, use \coloneqq from the mathtools package instead of “:=”.
[Thanks, this will be incorporated into the next revision of the ms. -T.]
1 February, 2013 at 10:19 am
Small doubling in groups « What’s new
[...] abelian case is discussed in this book of mine with Vu, and the nonabelian case discussed in this more recent book of mine), but instead focuses on the statements of the various known results, as well as some remaining [...]