5-dimensional geometries III: the fibered geometries

Andrew Geng

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arXiv · 1605.07546

5-dimensional geometries III: the fibered geometries

Andrew Geng

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Abstract

We classify the 5-dimensional homogeneous geometries in the sense of Thurston. The present paper (part 3 of 3) classifies those in which the linear isotropy representation is nontrivial but reducible. Most of the resulting geometries are products. Some interesting examples include a countably infinite family of inequivalent geometries diffeomorphic to $S^3 \times S^2$; 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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Andrew Geng. 2016-05-24. 5-dimensional geometries III: the fibered geometries. https://arxiv.org/abs/1605.07546

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