Related papers: A note on topological amenability

We give a simple proof for the rigidity of a complex in the bounded derived category of sheaves with constructible cohomology on an abelian variety.

We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.

Following the classical results of Stong, we introduce a cohomological analogue of a core of a finite sheaved topological space and propose an algorithm for simplification in this category. In particular we generalize the notion of beat…

Based on a simple example, it is explained how the homological analysis may be applied for modeling of the electric circuits. The homological branch, mesh and nodal analyses are presented. Geometrical interpretations are given.

The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global…

We look at topological equisingularity of a holomorphic family of reduced mapping germs f_t:(C^3,O)->C over a contractible base T having non-isolated singularities, by means of their normalisations. We introduce the notion of…

We develop a tighter implementation of basic PL topology, which keeps track of some combinatorial structure beyond PL homeomorphism type. With this technique we clarify some aspects of PL transversality and give combinatorial proofs of a…

This paper studies the homological bounds of gentle algebras, i.e., the upper bounds for the sum of the projective and injective dimensions of indecomposable modules over gentle algebras. We provide conditions under which this sum is…

We provide base change theorems, projection formulae and Verdier duality for both cohomology and homology in the context of finite topological spaces

Using the methods of Ozawa [4] and Runde [5], we show that a type I von Neumann algebra is approximately amenable if and only if it is amenable.

The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…

In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].

In this paper the concepts of character contractibility, approximate character amenability (contractibility) and uniform approximate character amenability (contractibility) are introduced. We are concerned with the relations among the…

We prove that the Bredon homology or cohomology of the partition complex with fairly general coefficients is either trivial or computable in terms of constructions with the Steinberg module. The argument involves developing a theory of…

We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…

We remark some basic facts on homological aspects of involutive Lie bialgebras and their involutive bimodules, and present some problems on surface topology related to these facts.

The present paper describes a way to relate Martin boundaries on spaces of varying topology. This enables us to approach some detailed inductive analysis of the eigenfunctions of conformal Laplacians on minimal hypersurfaces near their…

We establish a new homological lower bound for the Thurston norm on 1-cohomology of 3-manifolds. This generalizes previous results of C. McMullen, S. Harvey, and the author. We also establish an analogous lower bound for 1-cohomology of…

We use rewriting systems to spell out cup-products in the (twisted) cohomology groups of a product of surface groups. This allows us to detect a non-trivial obstruction bounding from below the effective topological complexity of an…

We classify simply connected, closed cohomogeneity one manifolds with singly generated or 4-periodic rational cohomology and positive Euler characteristic.