Related papers: Ends and simple coarse structures

Coarse geometry is the study of large-scale properties of spaces. In this paper we study group coarse structures (i.e., coarse structures on groups that agree with the algebraic structures), by using group ideals. We introduce a large class…

For each arbitrary finite group $G$, we consider a suitable notion of Gromov Hausdorff distance between compact $G$ metric spaces and derive lower bounds based on equivariant topology methods. As applications, we prove equivariant rigidity…

For any intrinsic Gromov hyperbolic space we establish a Gehring-Hayman type theorem for conformally deformed spaces. As an application, we prove that any complete intrinsic hyperbolic space with atleast two points in the Gromov boundary…

The Fredholm representation theory is well adapted to construction of homotopy invariants of non simply connected manifolds on the base of generalized Hirzebruch formula. Earlier a natural family of the Fredholm representations was…

In this paper, as a continuation of [30], we consider the Gromov-Hausdorff convergence and collapsing in the family of compact Riemannian manifolds with boundary satisfying lower bounds on the sectional curvatures of interior manifolds,…

We establish a regularity result for the metric on any 4-dimensional extremal K\"ahler manifold, and a weak compactness theorem on the space of such metrics. Specifically, the sectional curvature at a point is bounded when the quantity…

In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…

There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…

We classify compact surfaces with torsion-free affine connections for which every geodesic is a simple closed curve. In the process, we obtain completely new proofs of all the major results concerning the Riemannian case. In contrast to…

The causal boundary construction of Geroch, Kronheimer, and Penrose has some universal properties of importance for general studies of spacetimes, particularly when equipped with a topology derived from the causal structure. Properties of…

In our previous paper, we gave a complete list of the finite non-abelian simple groups whose holomorph contains a solvable regular subgroup. In this paper, we refine our previous work by considering all finite almost simple groups. In…

We investigate the local structure of the space $\mathcal{M}$ consisting of isometry classes of compact metric spaces, endowed with the Gromov-Hausdorff metric. We consider finite metric spaces of the same cardinality and suppose that these…

In arXiv math.MG/0207296 we introduced a product construction for locally compact, complete, geodesic hyperbolic metric spaces. In the present paper we define the hyperbolic product for general Gromov-hyperbolic spaces. In the case of…

We prove a partial generalization of Bonahon's tameness result to surfaces inside irreducible 3-manifolds with hyperbolic fundamental group. Bonahon's result states that geometrically infinite ends of freely indecomposable hyperbolic…

We investigate the geometry of the family $\cal M$ of isometry classes of compact metric spaces, endowed with the Gromov-Hausdorff metric. We show that sufficiently small neighborhoods of generic finite spaces in the subspace of all finite…

We construct secondary cup and cap products on coarse (co-)homology theories from given cross and slant products. They are defined for coarse spaces relative to weak generalized controlled deformation retracts. On ordinary coarse…

We introduce the notion of a manifold admitting a simple compact Cartan 3-form $\om^3$. We study algebraic types of such manifolds specializing on those having skew-symmetric torsion, or those associated with a closed or coclosed 3-form…

We introduce large scale analogues of topological monotone and light maps, which we call coarsely monotone and coarsely light maps respectively. We show that these two classes of maps constitute a factorization system on the coarse…

We give a proof of the Gromov compactness theorem using the language of stable curves (i.e. cusp-curve of Gromov, or stable maps of Kontsevich and Manin) in general setting: An almost complex structure on a target manifold is only…

We consider the asymptotic behavior of properly embedded minimal surfaces in the product of the hyperbolic plane with the line, taking into account the fact that there is more than one natural compactification of this space. This provides a…