Related papers: Finite-dimensional spaces in resolving classes

We give a new proof, using comparatively simple techniques, of the Sullivan conjecture: the space of pointed maps from the classifying space of the cyclic group of order $p$ to any finite-dimensional CW complex $K$ is contractible.

The simplest condition characterizing quasi-finite CW complexes $K$ is the implication $X\tau_h K\implies \beta(X)\tau K$ for all paracompact spaces $X$. Here are the main results of the paper: Theorem: If $\{K_s\}_{s\in S}$ is a family of…

We give a proof to the following theorem, which is well-known among experts: A connected subcomplex $W$ of a finite dimensional CAT(0) cubed complex $X$ is convex if and only if Lk$(v, W)$ is a full subcomplex of Lk$(v, X)$ for every vertex…

We extend the definition of quasi-finite complexes by considering not necessarily countable complexes. We provide a characterization of quasi-finite complexes in terms of L-invertible maps and dimensional properties of compactifications.…

A countable CW complex $K$ is quasi-finite (as defined by A.Karasev) if for every finite subcomplex $M$ of $K$ there is a finite subcomplex $e(M)$ such that any map $f:A\to M$, where $A$ is closed in a separable metric space $X$ satisfying…

We prove that for every compactum X with dim_Z X <= n >= 2 there is a cell-like resolution r: Z --> X from a compactum Z onto X such that dim Z <= n and for every integer k and every abelian group G such that dim_G X <= k >= 2 we have dim_G…

In this note we introduce the concept of a quasi-finite complex. Next, we show that for a given countable and locally finite CW complex L the following conditions are equivalent: (i) L is quasi-finite. (ii) There exists a [L]-invertible…

A finite $CW$-complex $X$ is $C$-trivial if for every complex vector bundle $\xi$ over $X$, the total Chern class $c(\xi)=1$. In this note we completely determine when each of the following spaces are $C$-trivial: suspensions of stunted…

Given CW complexes X and Y, let map(X,Y) denote the space of continuous functions from X to Y with the compact open topology. The space map(X,Y) need not have the homotopy type of a CW complex. Here the results of an extensive investigation…

Let F_*(X, Y) be the space of base-point-preserving maps from a connected finite CW complex X to a connected space Y. Consider a CW complex of the form X cup_{alpha}e^{k+1} and a space Y whose connectivity exceeds the dimension of the…

Let X be a finite CW complex. We show that the fundamental group of X is large if and only if there is a finite cover Y of X and a sequence of finite abelian covers \{Y_N\} of Y which satisfy b_1(Y_N)\geq N. We give some applications of…

In extension theory, in particular in dimension theory, it is frequently useful to represent a given compact metrizable space X as the limit of an inverse sequence of compact polyhedra. We are going to show that, for the purposes of…

A finite connected CW complex which is a co-H-space is shown to have the homotopy type of a wedge of a bunch of circles and a simply-connected finite complex after almost $p$-completion at a prime $p$.

We prove that if $B\subseteq A$ is an extension of finite dimensional algebras such that the projective dimension of $A/B$ as a $B$-bimodule is finite, if $A$ has finite finitistic dimension, then so does $B$. We exhibit examples…

In this paper, we establish the rationality conjecture raised in \cite{FKS} for any $(r-1)$-connected ($r\geq 2$) $kr$-dimensional CW-complex $X$ ($k\geq 2$) having a unique spherical cohomology class $u\in \tilde{H}^r(X, \mathbb{Z})$ such…

For a 1-connected CW-complex $X$, let $\mathcal{E}(X)$ denote the group of homotopy classes of self-homotopy equivalences of $X$. The aim of this paper is to prove that, for every $n\in\Bbb N$, there exists a 1-connected rational CW-complex…

Let $X$ be a (real or complex) infinite dimensional linear space. We establish conditions on a homogeneous polynomial $P$ on $X$ so that, if $W$ is any finite dimensional subspace of $X$ on which $P$ vanishes, then $P$ vanishes on an…

We prove existence of extension dimension for paracompact spaces. Here is the main result of the paper: \proclaim{Theorem} Suppose X is a paracompact space. There is a CW complex K such that {a.} K is an absolute extensor of X up to…

When a non-singular complex projective surface $X$ satisfies that $K_X\sim 0$, we shall show that there are only finitely many isomorphic classes as abstract schemes in the set of moduli scheme of $H$-semistable sheaves with fixed Chern…

We show that Sullivan's model of rational differential forms on a simplicial set $X$ may be interpreted as a (kind of) $0|1$-dimensional supersymmetric quantum field theory over $X$, and, as a consequence, concordance classes of such…