Related papers: Some remarks about solenoids, 2

We give an optimal bound on normal curvatures of immersed n-torus in a Euclidean ball of large dimension.

We survey some results on homological dimensions of the algebraic, complex analytic, and smooth quantum tori. Our main theorem states, in particular, that the smooth and the complex analytic quantum n-tori have global dimension n. This…

This item from the News & Views category, to be published in Light: Science & Applications, aims to provide a summary of theoretical and experimental results recently published in Ref. [24], which demonstrate the creation of corner modes in…

In this paper, a class of fractals, called quadrilateral labyrinth fractals, are introduced and studied. They are a special kind of fractals on any quadrilateral on the plane. This type of fractal is motivated by labyrinth fractal on the…

We analyze in detail projective modules over two-dimensional noncommutative tori and complex structures on these modules.We concentrate our attention on properties of holomorphic vectors in these modules; the theory of these vectors…

There are 6 types of 2-dimensional representations in general. For any groups and any monoids, we can construct the moduli of 2-dimensional representations for each type: the moduli of absolutely irreducible representations, representations…

Some one- and two-parametric deformations of U[sl(2)] and their representations are considered. Interestingly, a newly introduced two-parametric deformation admits a class of infinite - dimensional representations which have no classical…

We give a structure theorem for n-dimensional smooth toric Fano varieties whose associated polytope has "many" pairs of centrally symmetric vertices.

This is the second chapter in our "Toric Topology" book project. Further chapters are coming. Comments and suggestions are very welcome.

We have numerically calculated topological andnon-topological solitons in two spatial dimensions with Chern-Simons term. Their quantum stability, as well as that of the Maxwell vortex, is analyzed by means of bounce instantons which involve…

We study a relation between the Drinfeld modules and the even dimensional noncommutative tori. A non-abelian class field theory is developed based on this relation. Explicit generators of the Galois extensions are constructed.

We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.

A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.

The purpose of this article is to study an $f$-cosymplectic manifold $M$ admitting Ricci solitons. Here we consider mainly two classes of Ricci solitons on $f$-cosymplectic manifolds. One is the class of contact Ricci solitons. The other is…

We consider unimodality and related properties of f-vectors of polytopes in various dimensions. By a result of Kalai (1988), f-vectors of 5-polytopes are unimodal. In higher dimensions much less can be said; we give an overview on current…

In this paper, we give a method to describe the numerical class of a torus invariant surface on a projective toric manifold. As applications, we can classify toric 2-Fano manifolds of Picard number 2 or of dimension at most 4.

We study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non-archimedean amoebas. These compactifications have many nice properties, for example any k boundary…

We report on some recent results on a class of relativistic lagrangian field theories supporting non-topological soliton solutions and their applications in the contexts of Gravitation and Cosmology. We analyze one and many-components…

We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy.…

There is a construction which lies at the heart of descent theory. The combinatorial aspects of this paper concern the description of the construction in all dimensions. The description is achieved precisely for strict n-categories and…