Related papers: On Klein-Maskit Combination Theorem in space I

We develop a generalization of quantitative $K$-theory, which we call controlled $K$-theory. It is powerful enough to study the $K$-theory of crossed product of $C^*$-algebras by action of \'etale groupoids and discrete quantum groups. In…

We present a unified approach to (bi-)orthogonal basis sets for gravitating systems. Central to our discussion is the notion of mutual gravitational energy, which gives rise to the self-energy inner product on mass densities. We consider a…

A duality theorem for the category of locally compact Hausdorff spaces and continuous maps which generalizes the well-known Duality Theorem of de Vries is proved.

We discuss a very general Kirillov Theory for the representations of certain nilpotent groups which gives a combined view an many known examples from the literature.

We extend Elitzur's theorem to systems with symmetries intermediate between global and local. In general, our theorem formalizes the idea of {\it dimensional reduction}. We apply the results of this generalization to many systems that are…

We study a few basic properties of Banach-Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theory, we show that the notion of locally transitive Banach-Lie…

In this paper, we establish a Schmidt's subspace theorem for moving hypersurfaces in weakly subgeneral position. Our result generalizes the previous results on Schmidt's theorem for the case of moving hypersurfaces.

We generalise the Third Main Theorem by Brauer, the First and Second Fong Reduction to generalised block fusion systems and apply the Second Fong Reduction to extend a result by Cabanes about the non-exoticity of fusion systems of unipotent…

Combinatorial methods (or methods of elementary transformations) came to group theory from low-dimensional topology in the beginning of the century. Soon after that, combinatorial group theory became an independent area with its own…

In a recent paper by M. Mantoiu and M. Ruzhansky, a global pseudo-differential calculus has been developed for unimodular groups of type I. In the present article we generalize the main results to arbitrary locally compact groups of type I.…

In this paper, we introduce a discrete Riesz transforms associated with the non-symmetric trigonometric Heckman-Opdam polynomials of type $A_1$. We prove that they can be extended to a bounded operators on $\ell^p(\mathbb{Z})$,…

Using Klein's approach, geometry can be studied in terms of a space of points and a group of transformations of that space. This allows us to apply algebraic tools in studying geometry of mathematical structures. In this article, we follow…

In this paper, we present new applications of our general minimax theorems. In particular, one of them concerns the multiplicity of global minima for the integral functional of the Calculus of Variations.

In this paper we generalize previous work on decomposition in three-dimensional orbifolds by 2-groups realized as analogues of central extensions, to orbifolds by more general 2-groups. We describe the computation of such orbifolds in…

We introduce the theory of local minimal models for Kan simplicial manifolds, which provide the appropriate generalization of minimal Kan simplicial sets to geometric contexts. We use this to obtain the first proof of Lie's third theorem…

The Klein group contains only four elements. Nevertheless this little group contains a number of remarkable entry points to current highways of modern representation theory of groups. In this paper, we shall describe all possible ways in…

This paper is designed to attract people who work on real hyperbolic manifolds to consider thinking about discrete subgroups of higher rank Lie groups. To that end, we breezily discuss some applications of the ideas from the theory of…

We first propose a generalization of the image conjecture [Z3] for the commuting differential operators related with classical orthogonal polynomials. We then show that the non-trivial case of this generalized image conjecture is equivalent…

We show that the first two $k$-invariants of Top/O vanish and give some applications.

Mutually unbiased bases in Hilbert spaces of finite dimensions are closely related to the quantal notion of complementarity. An alternative proof of existence of a maximal collection of N+1 mutually unbiased bases in Hilbert spaces of prime…