Related papers: Surgery on discrete groups
We construct approximately inner actions of discrete amenable groups on strongly amenable subfactors of type II_1 with given invariants, and obtain classification results under some conditions. We also study the lifting of the relative \chi…
We study a geometric construction of certain finite index subgroups of Aut(F2).
We survey the recent applications and developments of sieve methods related to discrete groups, especially in the case of infinite index subgroups of arithmetic groups.
In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…
We study the collection of group structures that can be realized as a group of rational points on an elliptic curve over a finite field (such groups are well known to be of rank at most two). We also study various subsets of this collection…
We classify the subsets of a group by their sizes, formalize the basic methods of partitions and apply them to partition a group to subsets of prescribed sizes.
In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the action, and on the measure of fixed point sets, that imply…
We build and investigate a pure gauge theory on arbitrary discrete groups. A systematic approach to the construction of the differential calculus is presented. We discuss the metric properties of the models and introduce the action…
In this paper we use families of finite subgroups to study Grothendieck rings associated to certain discrete groups, such as the arithmetic ones.
This article focuses on the study of cut groups, i.e., the groups which have only trivial central units in their integral group ring. We provide state of art for cut groups. The results are compiled in a systematic manner and have also been…
We study groups, exponential groups and ordered groups equipped with valuations. We investigate algebraic and topological features of such valued structures, and apply our findings in order to solve regular equations over groups using…
We investigate continuous transitive actions of semitopological groups on spaces, as well as separately continuous transitive actions of topological groups.
This survey is based on a series of lectures that we gave at MSRI in Spring 2015 and on a series of papers, mostly written jointly with Joan Porti. Our goal here is to: 1. Describe a class of discrete subgroups $\Gamma<G$ of higher rank…
In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.
We survey and analyze different ways in which bornologies, coarse structures and uniformities on a group agree with the group operations.
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
We construct classifying spaces for discrete and compact Lie groups, with the property that they are topological groups and complete metric spaces in a natural way. We sketch a program in view of extending these constructions.
In this paper we discuss several results about the structure of the configuration space of two-dimensional tensegrities with a small number of points. We briefly describe the technique of surgeries that is used to find geometric conditions…
In this note we study the finite groups whose subgroup lattices are dismantlable.
In our previous works, we constructed diffeomorphisms of compact 4-manifolds $X$ by surgeries on theta-graphs embedded in $X$. In this paper, we consider the case $X=M\times I$, where $M$ is a spherical 3-manifold. For some of such $X$, we…