Discrete Group Actions and Generalized Real Bott Manifolds

We study a class of discrete group actions on the Euclidean space. In particular, we will investigate when the orbit spaces of such group actions are closed manifolds. The answer turns out to be a class of real toric manifolds called generalized real Bott manifolds which are the total spaces of some kind of iterated real projective space bundles. This relation provides a new viewpoint on generalized real Bott manifolds which might be useful for the future study.

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Published 20 February 2012