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arXiv · 1108.0293

Topology of iterated $S^1$-bundles

Jong Bum Lee·Mikiya Masuda
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Abstract

In this paper we investigate what kind of manifolds arise as the total spaces of iterated $S^1$-bundles. A real Bott tower studied in \cite{CMO}, \cite{KM} and \cite{KN} is an example of an iterated $S^1$-bundle. We show that the total space of an iterated $S^1$-bundle is homeomorphic to an infra-nilmanifold. A real Bott manifold, which is the total space of a real Bott tower, provides an example of a closed flat Riemannian manifold. We also show that real Bott manifolds are the only closed flat Riemannian manifolds obtained from iterated $\bbr{P}^1$-bundles. Finally we classify the homeomorphism types of the total spaces of iterated $S^1$-bundles in dimension 3.

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Jong Bum Lee, Mikiya Masuda. 2012-02-20. Topology of iterated $S^1$-bundles. https://arxiv.org/abs/1108.0293

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