Related papers: Finite-dimensional spaces in resolving classes

Let X be a finite CW complex or compact Lipschitz neighborhood retract with universal cover Z; let M be a compact orientable manifold of dimension at least 2 and nonempty boundary. We establish the existence of an isoperimetric profile for…

We consider Diophantine inequalities of the kind |f(x)| \le m, where F(X) \in Z[X] is a homogeneous polynomial which can be expressed as a product of d homogeneous linear forms in n variables with complex coefficients and m\ge 1. We say…

Effective bounds for the finite number of surjective holomorphic maps between canonically polarized compact complex manifolds of any dimension with fixed domain are proven. Both the case of a fixed target and the case of varying targets are…

Let $X\subset \mathbb{C}^n$ be a smooth irreducible affine variety of dimension $k$ and let $F: X\to \mathbb{C}^m$ be a polynomial mapping. We prove that if $m\ge k$, then there is a Zariski open dense subset $U$ in the space of linear…

The main theorem shows that if M is an irreducible compact connected orientable 3-manifold with non-empty boundary, then the classifying space BDiff(M rel dM) of the space of diffeomorphisms of M which restrict to the identity map on…

A map $f\colon K\to \mathbb R^d$ of a simplicial complex is an almost embedding if $f(\sigma)\cap f(\tau)=\emptyset$ whenever $\sigma,\tau$ are disjoint simplices of $K$. Theorem. Fix integers $d,k\ge2$ such that $d=\frac{3k}2+1$. (a)…

We prove that if a finite group $G$ contains a conjugacy class $K$ whose square is of the form $1 \cup D$, where $D$ is a conjugacy class of $G$, then $\langle K \rangle$ is a solvable proper normal subgroup of $G$ and we completely…

Given two finite abstract simplicial complexes A and B, one can define a new simplicial complex on the set of simplicial maps from A to B. After adding two technicalities, we call this complex Homsc(A, B). We prove the following dichotomy:…

We show that every discrete subgroup of $\mathrm{GL}(n,\mathbb{R})$ admits a finite dimensional classifying space with virtually cyclic stabilizers. Applying our methods to $\mathrm{SL}(3,\mathbb{Z})$, we obtain a four dimensional…

In this paper, we give a topological version of Scott convergence theorem for locally hypercompact spaces. We introduce the notion of $\mathcal{S}^*_X$-convergence on a $T_0$ topological space $X$, and define the notion of finitely…

We consider certain rational homotopical conditions of simly connected CW complex $X$ such that the rational cohomology of the classifying space $Baut_1X$ for fibrations with two-stage fibre $X$ is (not) free. First, we consider when is…

Let $L$ be a countable CW-complex and $F\colon X\to Y$ be upper semicontinuous $UV^{[L]}$-valued mapping of a paracompact space $X$ to a complete metric space $Y$. We prove that if $X$ is a C-space of extension dimension $\ed X \le [L]$,…

In response to a question raised by Belolipetsky and the first author, we prove that for every finite group $G$ there are infinitely many isomorphism classes of compact complex hyperbolic $2$-manifolds with automorphism group isomorphic to…

Let L be a countable and locally finite CW complex. Suppose that the class of all metrizable compacta of extension dimension not greater than L contains a universal element which is an absolute extensor in dimension L. Our main result shows…

For any $n\geq k\geq l\in\mathbb{N},$ let $S(n,k,l)$ be the set of all those non-negative definite matrices $a\in M_{n}(\mathbb{C})$ with $l\leq\text{rank }a\leq k$. Motivated by applications to $C^{*}$-algebra theory, we investigate the…

A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…

We prove the Categorified Wrapping Number Conjecture for large classes of annular links, including alternating annular links and tangle closures exhibiting plumbed link phenomena. We do so by characterizing when a resolution is sufficient…

We investigate the structure of finite groups whose non-central real class sizes have the same $2$-part. In particular, we prove that such groups are solvable and have $2$-length one. As a consequence, we show that a finite group is…

In this paper by using the ring of real-valued continuous functions $C(X)$, we prove a theorem in profinite spaces which states that for a compact Hausdorff space $X$, the set of its connected components $X/_{\sim}$ endowed with some…

Applying geometric methods of $2$-dimensional cell complex theory, we construct a Galois covering of a bimodule problem satisfying some structure, triangularity and finiteness conditions in order to describe the objects of finite…