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