Related papers: Transcendental simplicial volumes

The simplicial wedge construction on simplicial complexes and simple polytopes has been used by a variety of authors to study toric and related spaces, including non-singular toric varieties, toric manifolds, intersections of quadrics and…

We conjecture that for every dimension n not equal 3 there exists a noncompact hyperbolic n-manifold whose volume is smaller than the volume of any compact hyperbolic n-manifold. For dimensions n at most 4 and n=6 this conjecture follows…

The aim of this article is to show the existence, and also give an explicit construction, of infinite sets of orthogonal exponentials for certain families of convex polytopes which include simple-rational polytopes and also non simple…

We show that it is consistent that the continuum is as large as you wish, and for each uncountable cardinal $\kappa$ below the continuum, there are a subset $T$ of the reals and a family $A$ of countable subsets of $T$ such that (1) both…

Given an integer homology class of a finitely presentable group, the systolic volume quantifies how tight could be a geometric realization of this class. In this paper, we study various aspects of this numerical invariant showing that it is…

We discuss families of hypersurfaces with isolated singularities in projective space with the property that the sum of the ranks of the rational homotopy and the homology groups is finite. They represent infinitely many distinct homotopy…

We prove the existence of multiple closed geodesics on non-compact cylindrica manifolds.

In this paper, an n-dimensional complete open manifold with nonnegative Ricci curvature and collapsing volume has been investigated. If its radial sectional curvature bounded from below, it shows that such a manifold is of finite…

There exist simple dimension groups which cannot be expressed as a direct limit of simple, or even approximately divisible dimension groups, each with finitely many pure traces, and we can specify its infinite-dimensional Choquet simplex of…

We prove that complete non-locally symmetric quaternionic K\"ahler manifolds with an end of finite volume exist in all dimensions $4m\ge 4$.

We construct an explicit lower bound for the volume of a complex hyperbolic orbifold that depends only on dimension.

We look at a class of transcendental real numbers xi which, together with their square, satisfy some extremal property of simultaneous approximation by rational numbers with the same denominator. We give a sufficient condition for such a…

We consider simplicial sets equipped with a notion of smallness, and observe that this slight "topological" extension of the "algebraic" simplicial language allows a concise reformulation of a number of classical notions in topology, e.g.…

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or…

In this paper we introduce an enclosure of the numerical range of a class of rational operator functions. In contrast to the numerical range the presented enclosure can be computed exactly in the infinite dimensional case as well as in the…

Let $M^{n+1}$ be a closed manifold of dimension $3\le n+1\le 7$ equipped with a generic Riemannian metric $g$. Let $c$ be a positive number. We show that, either there exist infinitely many distinct closed hypersurfaces with constant mean…

A $(d-1)$-dimensional simplicial complex is called balanced if its underlying graph admits a proper $d$-coloring. We show that many well-known face enumeration results have natural balanced analogs (or at least conjectural analogs).…

It is proven that if a finitely presented group is one ended it has asymptotic dimension bigger than one. It follows that finitely presented groups with asdim 1 are virtually free. A counterexample is given for the finitely generated case.

In this paper, among other things, we prove that any subset of $\overline{\mathbb{Q}}^m$ (closed under complex conjugation and which contains the origin) is the exceptional set of uncountable many transcendental entire functions over…

Pseudoexponential fields are exponential fields similar to complex exponentiation satisfying the Schanuel Property, which is the abstract statement of Schanuel's Conjecture, and an adapted form of existential closure. Here we show that if…