Related papers: Some counterexamples in abstract coarse geometry
A general model for geometric structures on differentiable manifolds is obtained by deforming infinitesimal symmetries. Specifically, this model consists of a Lie algebroid, equipped with an affine connection compatible with the Lie…
The main objective of this article is to provide an alternative approach to the central result of [Eldred, A. Anthony, Kirk, W. A., Veeramani, P., Proximal normal structure and relatively nonexpansive mappings, Studia Math., vol 171(3),…
We compute the cohomology ring of a generalised type of configuration space of points in $\mathbb{R}^r$. This configuration space is indexed by a graph. In the case the graph is complete the result is known and it is due to Arnold and…
Divided into three parts, the first marks out enormous geometric issues with the notion of quasi-freenss of an algebra and seeks to replace this notion of formal smoothness with an approximation by means of a minimal unital commutative…
We establish sufficient conditions for finite convergence of the alternating projections method for two non-intersecting and potentially nonconvex sets. Our results are based on a generalization of the concept of intrinsic transversality,…
Spine spaces can be considered as fragments of a projective Grassmann space. We prove that the structure of lines together with binary coplanarity relation, as well as with binary relation of being in one pencil of lines, is a sufficient…
We adapt the construction of subsets of {1, 2, ..., N} that contain no k-term arithmetic progressions to give a relatively thick subset of an arbitrary set of N integers. Particular examples include a thick subset of {1, 4, 9, ..., N^2}…
We investigate how coarse embeddability of box spaces into Hilbert space behaves under group extensions. In particular, we prove a result which implies that a semidirect product of a finitely generated free group by a finitely generated…
Gravitational waves with a space-translation Killing field are considered. In this case, the 4-dimensional Einstein vacuum equations are equivalent to the 3-dimensional Einstein equations with certain matter sources. This interplay between…
For any compact Hausdorff space $K$ we construct a canonical finitary coarse structure $\mathcal E_{X,K}$ on the set $X$ of isolated points of $K$. This construction has two properties: $\bullet$ If a finitary coarse space $(X,\mathcal E)$…
This paper studies the asymptotic product of two metric spaces. It is well defined if one of the spaces is visual or if both spaces are geodesic. In this case the asymptotic product is the pullback of a limit diagram in the coarse category.…
We exhibit tight contact structures on 3-manifolds that do not admit any symplectic fillings.
In this note we prove that the Kalton interlaced graphs do not equi-coarsely embed into the James space $\mathcal J$ nor into its dual $\mathcal J^*$. It is a particular case of a more general result on the non equi-coarse embeddability of…
We establish a generalized analogue of the Boothby-Wang theorem in generalized contact geometry, along with related results. We present a general method for constructing examples of generalized contact structures that are not of Poon-Wade…
We show the non existence of manifold structure on certain topological constructions. The main results of this paper are: (1) The wedge of manifold with itself is not a manifold. (2) The cone of a manifold is not a manifold. The main tools…
Semi-entwining structures are proposed as concepts simpler than entwining structures, yet they are shown to have interesting applications in constructing intertwining operators and braided algebras, lifting functors, finding solutions for…
We show that there is an almost complex structure on a differential calculus on finite points coming from a bidirected finite graph without multiple edges or loops. We concentrate on a polygon as a concrete case. In particular, a…
In this paper, we introduce a notion of strongly quasi-local algebras. They are defined for each discrete metric space with bounded geometry, and sit between the Roe algebra and the quasi-local algebra. We show that strongly quasi-local…
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve has attracted much interest. In the present paper, we propose a new method to construct a surface…
It is well known that several classical geometry problems (e.g., angle trisection) are unsolvable by compass and straightedge constructions. But what kind of object is proven to be non-existing by usual arguments? These arguments refer to…