The classification of five-dimensional geometries /

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Bibliographic Details
Author / Creator:	Geng, Andrew Liang Li, author.
Imprint:	2016. Ann Arbor : ProQuest Dissertations & Theses, 2016
Description:	1 electronic resource (203 pages)
Language:	English
Format:	E-Resource Dissertations
Local Note:	School code: 0330
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11674562

Hidden Bibliographic Details
Other authors / contributors:	University of Chicago. degree granting institution.
ISBN:	9781339873275
Notes:	Advisors: Benson Farb; Danny Calegari. Dissertation Abstracts International, Volume: 77-12(E), Section: B. English
Summary:	We classify the 5-dimensional homogeneous geometries in the sense of Thurston. The 5-dimensional geometries with irreducible isotropy are the irreducible Riemannian symmetric spaces, while those with trivial isotropy are simply-connected solvable Lie groups of the form R3 x R2 or N x R where N is nilpotent. The geometries with nontrivial reducible isotropy are mostly products, but a number of interesting examples arise. These include a countably infinite family L(a;1) x S1 L(b;1) of inequivalent geometries diffeomorphic to S3 x S2, an uncountable family in which only a countable subfamily admits compact quotients, and the non-maximal geometry SO(4)/SO(2) realized by two distinct maximal geometries.

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