The classification of five-dimensional geometries /

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Bibliographic Details
Author / Creator:Geng, Andrew Liang Li, author.
Ann Arbor : ProQuest Dissertations & Theses, 2016
Description:1 electronic resource (203 pages)
Format: E-Resource Dissertations
Local Note:School code: 0330
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Other authors / contributors:University of Chicago. degree granting institution.
Notes:Advisors: Benson Farb; Danny Calegari.
Dissertation Abstracts International, Volume: 77-12(E), Section: B.
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.