Related papers: On Modular Gray Map
We prove the following two results for a given uniformly locally finite metric space with Yu's property A: 1) The group of outer automorphisms of its uniform Roe algebra is isomorphic to its group of bijective coarse equivalences modulo…
We describe explicitly the cohomology of the total complex of certain diagrams of invertible sheaves on normal toric varieties. These diagrams, called wheels, arise in the study of toric singularities associated to dimer models. Our main…
In this paper we give a small review of some recent results of elementary equivalence of linear and algebraic groups and our last new results of elementary equivalence of categories of modules, endomorphism rings of modules, lattices of…
We continue the analysis of the Modular Isomorphism Problem for $2$-generated $p$-groups with cyclic derived subgroup, $p>2$, started in [D. Garc\'ia-Lucas, \'A. del R\'io, and M. Stanojkovski. On group invariants determined by modular…
In this paper, a new general decomposition theory inspired from modular graph decomposition is presented. Our main result shows that, within this general theory, most of the nice algorithmic tools developed for modular decomposition are…
Geometrical structure of homogeneous isotropic models in the frame of the metric-affine gauge theory of gravity (MAGT) is analyzed. By using general form of gravitational Lagrangian including both a scalar curvature and various invariants…
Round fold maps are smooth maps on closed manifolds which are locally represented as the product maps of Morse functions and identity maps on open disks and whose singularity is realized as concentrically embedded spheres. The author…
A new generalization of the Gray map is introduced. The new generalization $\Phi: Z_{2^k}^n \to Z_{2}^{2^{k-1}n}$ is connected with the known generalized Gray map $\phi$ in the following way: if we take two dual linear $Z_{2^k}$-codes and…
Matrix congruence can be used to mimic linear maps between homogeneous quadratic polynomials in $n$ variables. We introduce a generalization, called standard-form congruence, which mimics affine maps between non-homogeneous quadratic…
This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization, each of these classical manifolds being…
We discuss invariants of Cohen-Macaulay local rings that admit a canonical module $\omega$. Attached to each such ring R, when $\omega$ is an ideal, there are integers--the type of R, the reduction number of $\omega$--that provide valuable…
The authors have used generalised Galois Theory to construct a homotopy double groupoid of a surjective fibration of Kan simplicial sets. Here we apply this to construct a new homotopy double groupoid of a map of spaces, which includes…
We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…
We develop a novel approach to gravity that we call `matrix general relativity' (MGR) or `gravitational chromodynamics' (GCD or GQCD for quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric…
The parametric geometry of numbers has allowed to visualize the simultaneous approximation properties of a collection of real numbers through the combined graph of the related successive minima functions. Several inequalities among…
We consider homogeneous spaces of Lie groups with compact stabilizer subgroups of two types: those with integrable invariant distributions and those with geodesic orbit invariant Riemannian metrics. The latter means that for an arbitrary…
We derive compact formulae for modular transformations of WZ characters. We start with algebra A_1 at positive level k=n-2, for which we can easily provide some description of isometry group and genus formula in a special case. We also…
This paper is primarily concerned with generalized reduced Verma modules over $\mathbb{Z}$-graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and the coinduced modules are obtained. Moreover, the…
We exhibit a smooth compactification of the moduli space of elliptic curves in a product of projective spaces with tangency along a subset of its toric boundary divisors. This is a Vakil--Zinger type of desingularization for maps to a…
A measure-scaling quasi-isometry between two connected graphs is a quasi-isometry that is quasi-$\kappa$-to-one in a natural sense for some $\kappa>0$. For non-amenable graphs, all quasi-isometries are quasi-$\kappa$-to-one for any…