Related papers: Gromov Ellipticity and subellipticity
In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…
We prove an analogue of Clifford's inequality for tropical curves. Next we focus on the hyperelliptic case and we characterize divisors attaining equality. Finally we speculate whether inequality in tropical Clifford's Theorem does imply…
In this note we classify simply connected rationally elliptic compact toric orbifolds up to algebraic isomorphism.
In this paper, considering the geometric equivalence for algebras of a variety $_{S}A$ of S-acts over a monoid S, we obtain representation theorems describing all types of the equivalence classes of geometrically equivalent S-acts of…
The manuscript is an overview of the motivations and foundations lying behind Voevodsky's ideas of constructing categories similar to the ordinary topological homotopy categories. The objects of these categories are strictly related to…
We will give a new proof for the Gromov's theorem on almost flat manifolds, which is an inductive proof on dimension.
V.I. Kopeiko proved that over a euclidean ring, the symplectic group defined with respect to the standard skew-symmetric matrix is same as the elementary symplectic group. Here we generalise the result of Kopeiko for a symplectic group…
We prove the infinitesimal version of Bishop-Gromov volume comparison condition for Alexandrov spaces.
We uncover a connection between two seemingly unrelated notions: lettericity, from structural graph theory, and geometric griddability, from the world of permutation patterns. Both of these notions capture important structural properties of…
We show the equivalence of two kinds of strict multiple category, namely the well known globular omega-categories, and the cubical omega-categories with connections.
Five geometrical eqivalents of Goldbach conjecture are given, calling one of them Fermat Like Theorem.
We study derived equivalences of Abelian varieties in terms of their associated symplectic data. For simple Abelian varieties over an algebraically closed field of characteristic zero we prove that the natural correspondence introduced by…
We match the elliptic genus of a Berglund-H\"ubsch model with the supertrace of $y^{J[0]}q^{L[0]}$ on a vertex algebra $V_{{\bf 1}, {\bf 1}}$. We show that it is a weak Jacobi form and the elliptic genus of one theory is equal to (up to a…
We show that the Gromov width of the Grassmannian of complex k-planes in C^n is equal to one when the symplectic form is normalized so that it generates the integral cohomology in degree 2. We deduce the lower bound from more general…
We study the isoperimetric problem in H-type groups and Grushin spaces, emphasizing a relation between them. We prove existence, symmetry and regularity properties of isoperimetric sets, under a symmetry assumption that depends on the…
This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more general notion of morphisms called infinity-morphisms. The…
In this paper, we prove some isoperimetric inequalities and give a sharp bound for the positive solution of sublinear elliptic equations.
We present a sharp version of the isoperimetric inequality for finitely generated groups due to T. Couhlon and L. Saloff-Coste based on the proof suggested by M. Gromov.
The relative Gromov seminorm is a finer invariant than stable commutator length where a relative homology class is fixed. We show a duality result between bounded cohomology and the relative Gromov seminorm, analogously to Bavard duality…
Every metric symplectic Lie algebra has the structure of a quadratic extension. We give a standard model and describe the equivalence classes on the level of corresponding quadratic cohomology sets. Finally, we give a scheme to classify the…