Related papers: Flat 2-orbifolds and Seifert fibred 4-manifolds

In this paper, we develop the theory for classifying all the geometric fibrations of compact, connected, flat $n$-orbifolds, over a 1-orbifold, up to affine equivalence. We apply our classification theory to classify all the geometric…

We explore algebraic characterizations of 2-knots whose associated knot manifolds fibre over lower-dimensional orbifolds, and consider also some issues related to the groups of higher-dimensional fibred knots.

In this paper we study three-dimensional orbifolds by 2-groups with a trivially-acting one-form symmetry group BK. These orbifolds have a global two-form symmetry, and so one expects that they decompose into (are equivalent to) a disjoint…

In early 1930s Seifert and Threlfall classified up to conjugacy the finite subgroups of $\mathrm{SO}(4)$, this gives an algebraic classification of orientable spherical 3-orbifolds. For the most part, spherical 3-orbifolds are Seifert…

Let G be an n-dimensional crystallographic group (n-space group). If G is a Z-reducible, then the flat n-orbifold E^n/G has a nontrivial fibered orbifold structure. We prove that this structure can be described by a generalized Calabi…

In this paper we describe the classification of all the geometric fibrations of a closed flat Riemannian 4-manifold over a 1-orbifold.

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…

We define the surface complex for $3$-manifolds and embark on a case study in the arena of Seifert fibered spaces. The base orbifold of a Seifert fibered space captures some of the topology of the Seifert fibered space, so, not…

Closed oriented 4-manifolds with the same geometrically 2-dimensional fundamental group (satisfying certain properties) are classified up to $s$-cobordism by their $w_2$-type, equivariant intersection form and the Kirby-Siebenmann…

We present about twenty conjectures, problems and questions about flat manifolds. Many of them build the bridges between the flat world and representation theory of the finite groups, hyperbolic geometry and dynamical systems.

This paper is a continuation of our previous paper, Co-Seifert fibrations of compact flat orbifolds, in which we developed the theory for classifying geometric fibrations of compact, connected, flat $n$-orbifolds, over a 1-orbifold, up to…

We show that if $B$ is an aspherical 2-orbifold in one of the families known to have orbifold fundamental groups of weight 1 then $B$ is the base of a Seifert fibration of a 2-knot manifold $M(K)$.

The first goal of this survey paper is to argue that if orbifolds are groupoids, then the collection of orbifolds and their maps has to be thought of as a 2-category. Compare this with the classical definition of Satake and Thurston of…

2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed curves where several sheets meet. They arise in the study of categorical invariants of 3-manifolds and may have applications to topological data…

The results of the paper concern the topological structure of complete riemannian manifolds with cyclic holonomy groups and low-dimensional orientable complete flat manifolds. We also discuss related results such as the affine…

We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz fibrations over S^2. The fibrations are necessarily hyperelliptic, and the resulting 4-manifolds are not even homotopy equivalent to complex surfaces. Furthermore,…

We consider the question of when is the closed manifold obtained by elementary surgery on an $n$-knot Seifert fibred over a 2-orbifold. After some observations on the classical case, we concentrate on the cases n=2 and 3. We have found a…

In [19] we studied a Fadell-Neuwirth type fibration theorem for orbifolds, and gave a short exact sequence of fundamental groups of configuration Lie groupoids of Lie groupoids corresponding to the genus zero 2-dimensional orbifolds with…

We describe all abelian groups which can appear as the fundamental groups of closed symplectically aspherical manifolds. The proofs use the theory of symplectic Lefschetz fibrations.

We give a purely geometrical smooth characterization of closed infrasolv manifolds and orbifolds by showing that, up to diffeomorphism, these are precisely the spaces which admit a collapse with bounded curvature and diameter to compact…