Related papers: Topological groups from matrices of sets
We develop a theory of large scale geometry of metrisable topological groups that, in a significant number of cases, allows one to define and identify a unique quasi-isometry type intrinsic to the topological group. Moreover, this…
A combinatorial map is a connected topological graph cellularly embedded in a surface. This monograph concentrates on the automorphism group of a map, which is related to the automorphism group of a Klein surface and a Smarandache manifold,…
This is a foundation for algebraic geometry, developed internal to the Zariski topos, building on the work of Kock and Blechschmidt. The Zariski topos consists of sheaves on the site opposite to the category of finitely presented algebras…
We develop a formalism that allows us to describe Markov compacta with finite sets of diagrams that are building blocks of the entire sequence. This encodes complex, continuous spaces with discrete collections of combinatorial objects. We…
We develop a framework to construct geometric representations of finite groups $G$ through the correspondence between real toric spaces $X^{\mathbb R}$ and simplicial complexes with characteristic matrices. We give a combinatorial…
The study of algebraic properties of groups of transformations of a manifold gives rise to an interplay between different areas of mathemathics such as topology, geometry, and dynamical systems. Especially, in this paper, we point out some…
Combinatorial Hopf algebras give a linear algebraic structure to infinite families of combinatorial objects, a technique further enriched by the categorification of these structure via the representation theory of families of algebras. This…
Groups with a topology that is in consistent one way or another with the algebraic structure are considered. Classical groups with a topology are topological, paratopological, semitopological, and quasitopological groups. We also study…
Topological full groups originated from the theory of topological dynamical systems and have been having considerable impact on group theory in recent years. This text represents an introduction/survey on topological full groups. After…
We consider the creation conditions of diverse hierarchical trees both analytically and numerically. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into a united structure…
A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such groups are called locally precompact. Within the class of locally…
We study groups of homeomorphisms of R, each of whose elements have at most one fixed point. In particular we prove that any such group of C^2 diffeomorphisms is topologically conjugate to an affine group.
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
A topological group is said to be ambitable if each uniformly bounded uniformly equicontinuous set of functions on the group with its right uniformity is contained in an ambit. For n=0,1,2,..., every locally aleph_n bounded topological…
In this paper, we investigate the topological full groups arising from the Cuntz and Cuntz-Toeplitz algebras and their crossed products with the Cartan subalgebras of Cuntz and Cuntz-Toeplitz algebras. We study the normal subgroups and…
We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
In the paper we discuss the algebraic structure of topological full group $[[T]]$ of a Cantor minimal system $(X,T)$. We show that the topological full group $[[T]]$ has the structure similar to a union of permutational wreath products of…
We describe constraints that need to be satisfied ``near the top'' of the portraits of the elements in Grigorchuk group. These constraints, if satisfied by the portraits of all sections of some binary tree automorphism, guarantee that this…
We use hyperbolic towers to answer some model theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the generic type $p_0$, but that there is a…