Related papers: A note on topological amenability
In which a theory of dimension related to the Jones index and based on the notion of conjugation is developed. An elementary proof of the additivity and multiplicativity of the dimension is given and there is an associated trace.…
The cohomology of a tiling or a point pattern has originally been defined via the construction of the hull or the groupoid associated with the tiling or the pattern. Here we present a construction which is more direct and therefore easier…
Amenable category is a variant of the Lusternik-Schnirelman category, based on covers by amenable open subsets. We study the monotonicity problem for degree-one maps and amenable category and the relation between amenable category and…
This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
We establish a characterization of amenability for general Hausdorff topological groups in terms of matchings with respect to finite uniform coverings. Furthermore, we prove that it suffices to just consider two-element uniform coverings.…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
Amenability is a geometric property of convex cones that is stronger than facial exposedness and assists in the study of error bounds for conic feasibility problems. In this paper we establish numerous properties of amenable cones, and…
A topological monoid is isomorphic to an endomorphism monoid of a countable structure if and only if it is separable and has a compatible complete ultrametric such that composition from the left is non-expansive. We also give a topological…
The aim of this short note is to develop a (co)homology theory for topological spaces together with the specialisation preorder. A known way to construct such a (co)homology is to define a partial order on the topological space starting…
We present a new approach to the amenability of groupoids (both in the measure theoretical and the topological setups) based on using Markov operators. We introduce the notion of an invariant Markov operator on a groupoid and show that the…
We study closed orientable manifolds whose topological complexity is at most 3 and determine their cohomology rings. For some of admissible cohomology rings we are also able to identify corresponding manifolds up to homeomorphism.
We analyze and compare different dynamical systems and groupoids which can be obtained from projection point patterns. We define the cohomology of a point pattern as the cocycle cohomology of the pattern groupoid. We describe this…
We define the topological pressure for any sub-additive potentials of the countable discrete amenable group action and any given open cover. A local variational principle for the topological pressure is established.
We will give a criterion for the amenability of arbitrary locally finite trees. The criterion is based on the trimming operator which is defined on the space of trees. As an application, we obtain a necessary and sufficient condition for…
In this paper we find some necessary and sufficient conditions for a Banach algebra to be amenable or weakly amenable, by applying the homomorphisms on Banach algebras.
On objects of a triangulated category with a stability condition, we construct a topology.
We revisit the notion of one-sided recognizability of morphisms and its relation to two-sided recognizability.
We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.
We express the rational cohomology of the unordered configuration space of a compact oriented manifold as a representation of its mapping class group in terms of a weight-decomposition of the rational cohomology of the mapping space from…
The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…