Related papers: Dyadic cubes in spaces of homogeneous type

Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…

We show that the variety of symmetric implication algebras is generated from cubic implication algebras and Boolean algebras. We do this by developing the notion of a locally symmetric implication algebra that has properties similar to…

We present period domains of complex Hodge structures and some of their basic properties from representation theory point of view. Specifically we introduce the automorphic cohomology of period domains and the complex structure on symmetric…

We construct triangular hyperbolic polyhedra whose links are generalized 4-gons. The universal cover of those polyhedra are hyperbolic buildings, which appartments are hyperbolic planes tesselated by regular triangles with angles $\pi/4$.…

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed…

We completely determine cohomology groups of sections of homogeneous line bundles over a toroidal group.

Let G be a reductive group over an algebraically closed field of characteristic p>0. We study properties of embeddings of spherical homogeneous G-spaces. We look at Frobenius splittings, canonical or by a (p-1)-th power, compatible with…

We construct two-dimensional families of complex hyperbolic structures on disc orbibundles over the sphere with three cone points. This contrasts with the previously known examples of the same type, which are locally rigid. In particular,…

We introduce two classes of homogeneous polynomials and show their role in constructing of integrable hierarchies for some integrable lattices.

Spaces of holomorphic maps from the Riemann sphere to various complex manifolds (holomorphic curves ) have played an important role in several area of mathematics. In a seminal paper G. Segal investigated the homotopy type of holomorphic…

We explain in some detail the geometric structure of spheres in any dimension. Our approach may be helpful for other homogeneous spaces (with other signatures) such as the de Sitter and anti-de Sitter spaces. We apply the procedure to the…

We work out the phase-space structure for a system of $n$ qubits. We replace the field of real numbers that label the axes of the continuous phase space by the finite field $\Gal{2^n}$ and investigate the geometrical structures compatible…

In this paper we will define notion homotopy of morphisms of crossed modules of Lie algebras. Then we construct a groupoid structure of Lie crossed module morphisms and their homotopies.

On a homogeneous group, we characterize the one-parameter groups of dilations whose associated Hardy spaces in the sense of Folland and Stein are the same.

This paper proves the existence of homeomorphic (diffeomorphic) complex 6-dimensional (7-dim) complete intersections that belong to components of the moduli space of different dimensions. These results are given as a supplement to earlier…

We determine a precise necessary and sufficient condition for completeness of the Hamiltonian vector field associated to a homogeneous cubic polynomial on a symplectic plane.

A holomorphic representation formula for special parabolic hyperspheres is given.

The moduli space of Higgs bundles can be constructed as a quotient of an infinite-dimensional space and hence admits an orbit type decomposition. In this paper, we show that the orbit type decomposition is a complex Whitney stratification…

We propose a definition of a quantum homogeneous space of a locally compact quantum group. We show that classically it reduces to the notion of a homogeneous spaces. On the quantum level our definition goes beyond the quotient case. It…

It is well known that the category of finite sets and cospans, composed by pushout, contains the universal {\em special} commutative Frobenius algebra. In this note we observe that the same construction yields also general commutative…