相关论文: On the $S^1$-fibred nil-Bott Tower
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…
If $B$ is a toric manifold and $E$ is a Whitney sum of complex line bundles over $B$, then the projectivization $P(E)$ of $E$ is again a toric manifold. Starting with $B$ as a point and repeating this construction, we obtain a sequence of…
A Bott tower is an iterated $\CP ^1$-bundle over a point, where each $\CP ^1$-bundle is the projectivization of a rank $2$ decomposable complex vector bundle. For a Bott tower, the filtered cohomology is naturally defined. We show that…
A Bott tower is the total space of a tower of fibre bundles with base CP^1 and fibres CP^1. Every Bott tower of height n is a smooth projective toric variety whose moment polytope is combinatorially equivalent to an n-cube. A circle action…
The main aim of this article is to study the topology of real Bott towers as special and interesting examples of real toric varieties. We first give a presentation of the fundamental group of a real Bott tower and show that the fundamental…
A Bott manifold is a closed smooth manifold obtained as the total space of an iterated $\C P^1$-bundle starting with a point, where each $\C P^1$-bundle is the projectivization of a Whitney sum of two complex line bundles. A…
A real Bott manifold is the total space of a sequence of $\R P^1$ bundles starting with a point, where each $\R P^1$ bundle is projectivization of a Whitney sum of two real line bundles. A real Bott manifold is a real toric manifold which…
A Seifert manifold is a 3-dimensional manifold with a circle action. It is a circle bundle (with singularities) over a 2-dimensional orbifold. In this note, we discuss a generalized Seifert manifolds. By definition, they have bundle-like…
Stiefel manifolds arise naturally as spaces of injective operators and as total spaces of principal bundles over Grassmannians. While their finite-dimensional topology is governed by Bott periodicity, the infinite-dimensional theory…
We give short proofs of the following two facts: Iterated principal circle bundles are precisely the nilmanifolds. Every iterated circle bundle is almost flat, and hence diffeomorphic to an infranilmanifold.
We prove a finiteness theorem for subgroups of bounded rank in hyperbolic $3$-manifold groups. As a consequence, we show that every bounded rank covering tower of closed hyperbolic $3$-manifolds is a tower of finite covers associated to a…
To a direct sum of holomorphic line bundles, we can associate two fibrations, whose fibers are, respectively, the corresponding full flag manifold and the corresponding projective space. Iterating these procedures gives, respectively, a…
A real Bott tower is obtained as the orbit space of the $n$-torus $T^n$ by the free action of an elementary abelian 2-group $(\mathbb{Z}_2)^n$. This paper deals with the classification of 5-dimensional real Bott towers and study certain…
Every compact aspherical Riemannian manifold admits a canonical series of orbibundle structures with infrasolv fibers which is called its infrasolv tower. The tower arises from the solvable radicals of isometry group actions on the…
We present a structural description of finite nilpotent groups of class at most $2$ using a specified number of subdirect and central products of $2$-generated such groups. As a corollary, we show that all of these groups are isomorphic to…
A Bott manifold is a smooth projective toric variety having an iterated $\mathbb{C} P^1$-bundle structure. A certain family of Bott manifolds is used to understand the structure of Bott--Samelson varieties (or…
We study fibrations in the category of cubespaces/nilspaces. We show that a fibration of finite degree $f \colon X\rightarrow Y$ between compact ergodic gluing cubespaces (in particular nilspaces) factors as a (possibly countable) tower of…
Plante-Thurston proved that every nilpotent subgroup of $\Diff^2(S^1)$ is abelian. One of our main results is a sharp converse: $\Diff^1(S^1)$ contains every finitely-generated, torsion-free nilpotent group.
Hirzebruch surfaces, defined as the projectivization of line bundles over $\C\mathbb{P}^1$, support a toric action and thus represent an infinite class of symplectic toric manifolds of complex dimension 2. In this paper, an infinite class…
A real Bott manifold is the total space of iterated RP^1 bundles starting with a point, where each RP^1 bundle is projectivization of a Whitney sum of two real line bundles. We prove that two real Bott manifolds are diffeomorphic if their…