相关论文: Good, but not very good orbifolds

Examples of nonformal simply connected symplectic manifolds are constructed.

For an orbifold, there is a notion of an orbifold embedding, which is more general than the one of sub-orbifolds. We develop several properties of orbifold embeddings. In the case of translation groupoids, we show that such a notion is…

We discuss properties of complex algebraic orbifold groups, their characteristic varieties, and their abelian covers. In particular, we deal with the question of (quasi)-projectivity of orbifold groups. We also prove a structure theorem for…

We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.

We review recent results concerning closed G$_2$-structures on seven-dimensional manifolds. In particular, we discuss the construction of examples and some related problems.

We construct infinitely many manifolds admitting both strongly irreducible and weakly reducible minimal genus Heegaard splittings. Both closed manifolds and manifolds with boundary tori are constructed.

In this note we prove that any closed graph manifold admitting a metric of non-positive sectional curvature (NPC-metric) has a finite cover, which is fibered over the circle. An explicit criterion to have a finite cover, which is fibered…

We prove that a contractible orbifold is a manifold.

We construct 3-manifolds which have at least two inequivalent embeddings such that both complementary regions have abelian fundamental group.

We prove the existence of multiple closed geodesics on non-compact cylindrica manifolds.

To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.

In this article we construct closed, isospectral, non-isometric locally symmetric manifolds. We have three main results. First, we construct arbitrarily large sets of closed, isospectral, non-isometric manifolds. Second, we show the growth…

We give examples of harmonic maps between negatively curved manifolds with special properties. These negatively curved manifolds do not have the homotopy type of a locally symmetric space.

In any dimension at least five we construct examples of closed smooth manifolds with the following properties: 1) they have neither real projective nor flat conformal structures; 2) their fundamental group is a non-elementary Gromov…

We provide the first non-trivial examples of quasi-isometric embeddings between curve complexes. These are induced either by puncturing a closed surface or via orbifold coverings. As a corollary, we give new quasi-isometric embeddings…

This work concludes a series of four papers on the foundational theory of orbifolds and stacks. We apply the abstract theory, developed in its predecessors, to orbifolds derived from manifolds. Specifically, we show how the very concrete…

For each $n\geq 3$ we give examples of infinitesimally rigid projective manifolds of general type of dimension $n$ with non-contractible universal cover. We provide examples with projective and examples with non-projective universal cover.

The aim of this paper is two-fold. First, the study of $C_{12}$-structure (called by us corner structure) is extended to the general case without any condition, unlike our previous papers (see, \cite{BB, BG2, BG, BBB}). Second, starting…

We exhibit a closed aspherical 5-manifold of nonpositive curvature that fibers over a circle whose fundamental group is hyperbolic relative to abelian subgroups such that the fiber is a closed aspherical 4-manifold whose fundamental group…

This exploratory paper considers the notion of a covering of a configuration and $G$-coverings which are coverings that are quotients under a semi-regular group action. We consider prime configurations, those which cannot $G$-cover other…