Related papers: Continuous Association Schemes and Hypergroups
We establish a connection between continuous K-theory and integral cohomology of rigid spaces. Given a rigid analytic space over a complete discretely valued field, its continuous K-groups vanish in degrees below the negative of the…
The purpose of the present article is threefold. First of all, we rebuild the whole theory of cosimplicial models of mapping spaces by using systematically Kan adjunction techniques. Secondly, given two topological spaces X and Y, we…
In [1] we defined a new kind of space called 'structured space' which locally resembles, near each of its points, some algebraic structure. We noted in the conclusion of the cited paper that the maps $f_s$ and $h$, which are of great…
A continuous infinite system of point particles with strong superstable interaction is considered in the framework of classical statistical mechanics. The family of approximated correlation functions is determined in such a way, that they…
We propose a novel construction of finite hypergraphs and relational structures that is based on reduced products with Cayley graphs of groupoids. To this end we construct groupoids whose Cayley graphs have large girth not just in the usual…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
The schematic finite spaces are those finite ringed spaces where a theory of quasi-coherent modules can be developed with minimal natural conditions. We give various characterizations of these spaces and their natural morphisms. We show…
Lattice discretizations of continuous manifolds are common tools used in a variety of physical contexts. Conventional discrete approximations, however, cannot capture all aspects of the original manifold, notably its topology. In this paper…
This article is part of the program of studying large-scale geometric properties of totally disconnected locally compact groups, TDLC-groups, by analogy with the theory for discrete groups. We provide a characterization of hyperbolic…
Hughes defined a class of groups that act as local similarities on compact ultrametric spaces. Guba and Sapir had previously defined braided diagram groups over semigroup presentations. The two classes of groups share some common…
Classical Ramsey theory has successfully extended to relational structures, yielding a wealth of results that have profoundly influenced other areas of mathematics. Interestingly, the same development has not occurred in the case of dual…
The article covers developments in the representation theory of finite group schemes over the last fifteen years. We start with the finite generation of cohomology of a finite group scheme and proceed to discuss various consequences and…
We show that one can define and effectively compute Stallings graphs for quasi-convex subgroups of automatic groups (\textit{e.g.} hyperbolic groups or right-angled Artin groups). These Stallings graphs are finite labeled graphs, which are…
We show that for topological groups and loop contractible coefficients the cohomology groups of continuous group cochains and of group cochains that are continuous on some identity neighbourhood are isomorphic. Moreover, we show a similar…
In the present paper, we show that many combinatorial and topological objects, such as maps, hypermaps, three-dimensional pavings, constellations and branched coverings of the two--sphere admit any given finite automorphism group. This…
Hierarchically hyperbolic spaces provide a common framework for studying mapping class groups of finite type surfaces, Teichm\"uller space, right-angled Artin groups, and many other cubical groups. Given such a space $\mathcal X$, we build…
We define novel fully combinatorial models of higher categories. Our definitions are based on a connection of higher categories to "directed spaces". Directed spaces are locally modelled on manifold diagrams, which are stratifications of…
To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…
Conformal inclusions of chiral conformal field theories, or more generally inclusions of quantum field theories, are described in the von Neumann algebraic setting by nets of subfactors, possibly with infinite Jones index if one takes…
We define and study several new interleaving distances for persistent cohomology which take into account the algebraic structures of the cohomology of a space, for instance the cup product or the action of the Steenrod algebra. In…