Related papers: Convergence actions and Specker compactifications
We develop a coarse notion of bundle and use it to understand the coarse geometry of group extensions and, more generally, groups acting on proper metric spaces. The results are particularly sharp for groups acting on (locally finite) trees…
Spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric…
We study algebraic actions of finite groups of quiver automorphisms on moduli spaces of quiver representations. We decompose the fixed loci using group cohomology and we give a modular interpretation of each component. As an application, we…
Group contraction is an algebraic map that relates two classes of Lie groups by a limiting process. We utilize this notion for the compactification of the class of Cartan motion groups. The compactification process is then applied to reduce…
The survey presents developments in the theory of self-similar groups leading to applications to the study of fractal sets and graphs, and their associated spectra.
We define compactifications of vector spaces which are functorial with respect to certain linear maps. These "many-body" compactifications are manifolds with corners, and the linear maps lift to b-maps in the sense of Melrose. We derive a…
In this paper, we study compact complex orbifolds. In the first part, we shows the equivalence of two notions of compact K\"ahler orbifold. In the second part, we shows various versions of Demailly's regularisation theorems for compact…
We introduce a new integral invariant for isometric actions of compact Lie groups, the copolarity. Roughly speaking, it measures how far from being polar the action is. We generalize some results about polar actions in this context. In…
The aim of the note is to extend the uniformization theorem to compact Kahler spaces X with mild singularities and establish a kind of rigidity of their universal coverings. We assume the fundamental group of X is large, residually finite…
Ellis's "functional approach" allows one to obtain proper compactifications of a topological group $G$ if $G$ can be represented as a subgroup of the homeomorphism group of a space $X$ in the topology of pointwise convergence and $G$-space…
The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.
The purpose of this article is to study operators whose kernel share some key features of Bergman kernels from complex analysis, and are approximate projectors. It turns out that they must be associated with a rich set of geometric data, on…
We study glued tensor and free products of compact matrix quantum groups with cyclic groups -- so-called tensor and free complexifications. We characterize them by studying their representation categories and algebraic relations. In…
The compactness phenomenon is one of the featured aspects of structuralism in mathematics. In simple and broad words, a compactness property holds in a structure if a related property is satisfied by sufficiently many substructures of that…
The light amplification by finite active media is used extensively in modern optics applications. In this paper the light amplification and scattering by cluster of small particles is studied analytically and numerically with the help of…
In a series of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In particular, we introduced the notion of…
We introduce a notion of stratification for rigidly-compactly generated tensor-triangulated categories relative to the homological spectrum and develop the fundamental features of this theory. In particular, we demonstrate that it exhibits…
In this note, we investigate a mixture of combinatorial spectra and stratified simplicial sets, which would be thought of as a model of the spectrum objects of $(\infty, \infty)$-categories.
This paper introduces a generalization of Pontryagin duality for locally compact Hausdorff abelian groups to locally compact Hausdorff abelian group bundles.
We develop the fundamental theory to study cubical isometry groups as totally disconnected, locally compact groups. We show how cubical isometries are determined by their local actions and how this can be applied in explicit constructions.…