Related papers: Good, but not very good orbifolds

We give examples of anomalous two-fold coverings $p:E\to B$ of connected spaces: a. one where $B$ is simply connected, b. the other of path-connected spaces that has an Evil Twin; a non equivalent covering $q:E\to B$ with the same image of…

We construct pairs of compact Riemannian orbifolds which are isospectral for the Laplace operator on functions such that the maximal isotropy order of singular points in one of the orbifolds is higher than in the other. In one type of…

In this paper, a lot of examples of four-dimensional manifolds with an almost hypercomplex pseudo-Hermitian structure are constructed in several explicit ways. The received 4-manifolds are characterized by their linear invariants in the…

We give a condition for an almost constant-type manifold to be a constant-type manifold, and holomorphic and $R$-invariant submanifolds of almost Hermitian manifolds are studied. Generalizations of some results in [5] are given.

A Riemannian manifold is called almost positively curved if the set of points for which all $2$-planes have positive sectional curvature is open and dense. We find three new examples of almost positively curved manifolds: $Sp(3)/Sp(1)^2$,…

A foliation of a manifold M is called R-covered if its lift to the universal cover of M has space of leaves R. We show that there are many graph manifolds which admit taut foliations, but which do not admit any R-covered foliations. On the…

There are examples of branched surfaces that do not fully carry laminations, but their preimage in a finite cover does fully carry a lamination

We give obstructions for a noncompact manifold to admit a complete Riemannian metric with (nonuniformly) positive scalar curvature. We treat both the finite volume and infinite volume cases.

This paper grew out of an attempt to find a suitable finite sheeted covering of an aspherical 3-manifold so that the cover either has infinite or trivial first homology group. With this motivation we define a new class of groups. These…

We construct a compact manifold with a closed $G_2$ structure not admitting any torsion-free $G_2$ structure, which is non-formal and has first Betti number $b_1=1$. We develop a method of resolution for orbifolds that arise as a quotient…

We prove the following result: Let $(X,g_0)$ be a complete, connected 4-manifold with uniformly positive isotropic curvature and with bounded geometry. Then there is a finite collection $\mathcal{F}$ of manifolds of the form $\mathbb{S}^3…

We give a sufficient condition to rule out complete Riemannian metrics with nonnegative scalar curvature on the interiors of handlebodies. In higher dimensions, we give examples of ends of manifolds with positive scalar curvature metrics.

The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous…

After a short summary of known results on surface-complexity of closed 3-manifolds, we will classify all closed orientable 3-manifolds with surface-complexity one.

Deformation theory of complex manifolds is a classical subject with recent new advances in the noncompact case using both algebraic and analytic methods. In this note, we recall some concepts of the existing theory and introduce new notions…

This is an example on the cohomology of threefolds.

In this paper, an n-dimensional complete open manifold with nonnegative Ricci curvature and collapsing volume has been investigated. If its radial sectional curvature bounded from below, it shows that such a manifold is of finite…

In this note, we consider contractible loops of contactomorphisms that are positive over some non-empty closed subset of a contact manifold. Such closed subsets are called immaterial. We argue that the complement of a Reeb-invariant…

We prove the following result: Let $(\mathcal{O},g_0)$ be a complete, connected 3-orbifold with uniformly positive scalar curvature, with bounded geometry, and containing no bad 2-suborbifolds. Then there is a finite collection…

We construct examples of elliptic fibrations of orbifold general type (in the sense of Campana) which have no etale covers dominating a variety of general type.