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January 2014 On the $S^{1}$-fibred nilBott tower
Mayumi Nakayama
Osaka J. Math. 51(1): 67-89 (January 2014).

Abstract

We shall introduce a notion of $S^{1}$-fibred nilBott tower. It is an iterated $S^{1}$-bundle whose top space is called an $S^{1}$-fibred nilBott manifold and the $S^{1}$-bundle of each stage realizes a Seifert construction. The $S^{1}$-fibred nilBott tower is a generalization of real Bott tower from the viewpoint of fibration. In this note we shall prove that any $S^{1}$-fibred nilBott manifold is diffeomorphic to an infranilmanifold. According to the group extension of each stage, there are two classes of $S^{1}$-fibred nilBott manifolds which is defined as finite type or infinite type. We discuss their properties.

Citation

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Mayumi Nakayama. "On the $S^{1}$-fibred nilBott tower." Osaka J. Math. 51 (1) 67 - 89, January 2014.

Information

Published: January 2014
First available in Project Euclid: 8 April 2014

zbMATH: 1296.55016
MathSciNet: MR3192532

Subjects:
Primary: 51M10 , 53C55 , 57S25

Rights: Copyright © 2014 Osaka University and Osaka City University, Departments of Mathematics

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Vol.51 • No. 1 • January 2014
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