On the $S^1$-fibred nil-Bott Tower

Details On the $S^1$-fibred nil-Bott Tower On the $S^1$-fibred nil-Bott Tower

2011-10-06

arxiv.org/abs/1110.1164v1

Mathematics

Algebraic Topology

20 pages

Scientific paper

We shall introduce a notion of $S^1$-fibred nilBott tower. It is an iterated $S^1$-bundles whose top space is called an $S^1$-fibred nilBott manifold and the $S^1$-bundle of each stage realizes a Seifert construction. The 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.

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