Related papers: Coarse Homotopy Groups

In the rational cohomology of a 1-connected space a structure of $C_{\infty}$-algebra is constructed and it is shown that this object determines the rational homotopy type

We introduce some compact orbifolds on which there is a certain finite group action having a simple convex polytope as the orbit space. We compute the orbifold fundamental group and homology groups of these orbifolds. We calculate the…

Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…

We study the geometry of warped cones over free, minimal isometric group actions and related constructions of expander graphs. We prove a rigidity theorem for the coarse geometry of such warped cones: Namely, if a group has no abelian…

For a complex projective space the inertia group, the homotopy inertia group and the concordance inertia group are isomorphic. In complex dimension 4n+1, these groups are related to computations in stable cohomotopy. Using stable homotopy…

In this paper, we define (reduced) homeology groups and (reduced) cohomeology groups on finite simpicial complexes and prove that these groups are PL homeomorphsm invariants of polyhedra, while they are not homotopy invariants. So these…

We describe the groups that have the same holomorph as a finite perfect group. Our results are complete for centerless groups. When the center is non-trivial, some questions remain open. The peculiarities of the general case are illustrated…

For a Kan complex with a vertex, we have the notion of its simplicial homotopy groups. In this paper, for a weak complicial set in the sense of Verity with a vertex, we construct monoids which are a generalization of simplicial homotopy…

We introduce an alternative description of coarse proximities. We define a coarse normality condition for connected coarse spaces and show that this definition agrees with large scale normality defined in [3] and asymptotic normality…

For a $C^{*}$-category with a strict $G$-action we construct examples of equivariant coarse homology theories. To this end we first introduce versions of Roe categories of objects in $C^{*}$-categories which are controlled over bornological…

We prove several positive results regarding representation of homotopy classes of spheres and algebraic groups by regular mappings. Most importantly we show that every mapping from a sphere to an orthogonal or a unitary group is homotopic…

This monograph introduces a framework for genuine proper equivariant stable homotopy theory for Lie groups. The adjective `proper' alludes to the feature that equivalences are tested on compact subgroups, and that the objects are built from…

In this short note we show that the homotopy category of smooth compactifications of smooth algebraic varieties is equivalent to the homotopy category of smooth varieties over a field of characteristic zero. As an application we show that…

We prove that the simplicial cocommutative coalgebra of singular chains on a connected topological space determines the homotopy type rationally and one prime at a time, without imposing any restriction on the fundamental group. In…

We explain how the notion of homotopy colimits gives rise to that of mapping spaces, even in categories which are not simplicial. We apply the technique of model approximations and use elementary properties of the category of spaces to be…

Given based cellular spaces X and Y, X compact, we define a sequence of increasingly fine equivalences on the based-homotopy set [X,Y].

We define a homotopy relation between arrows of a category with weak equivalences, and give a condition under which the quotient by the homotopy relation yields the homotopy category. In the case of the fibrant-cofibrant objects of a model…

A coarse group is a group endowed with a coarse structure so that the group multiplication and inversion are coarse mappings. Let $(X, \mathcal{E})$ be a coarse space and let $\mathfrak{M}$ be a variety of groups different from the variety…

The usual way of defining weak equivalences for simplicial presheaves is to require an isomorphism on all sheaves of homotopy groups. We unravel some of the machinery here, and give a more concrete description in terms of local homotopy…

We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a…