Topology of iterated $S^1$-bundles
Algebraic Topology
2013-12-30 v2 Differential Geometry
Geometric Topology
Abstract
In this paper we investigate what kind of manifolds arise as the total spaces of iterated -bundles. A real Bott tower studied in \cite{CMO}, \cite{KM} and \cite{KN} is an example of an iterated -bundle. We show that the total space of an iterated -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 -bundles. Finally we classify the homeomorphism types of the total spaces of iterated -bundles in dimension 3.
Keywords
Cite
@article{arxiv.1108.0293,
title = {Topology of iterated $S^1$-bundles},
author = {Jong Bum Lee and Mikiya Masuda},
journal= {arXiv preprint arXiv:1108.0293},
year = {2013}
}