Related papers: Relative cell complexes in closure spaces
The paper deals with the program of determining the complexity of various homeomorphism relations. The homeomorphism relation on compact Polish spaces is known to be reducible to an orbit equivalence relation of a continuous Polish group…
Any unital separable continuous C(X)-algebra with properly infinite fibres is properly infinite as soon as the compact Hausdorff space X has finite topological dimension. We study conditions under which this is still the case in the…
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…
The (co)homology self-closeness number of a simply-connected based CW-complexes $X$ is the minimal number $k$ such that any self-map $f$ of $X$ inducing an automorphism of the (co)homology groups for dimensions$\leq k$ is a self-homotopy…
For a closed connected oriented manifold $M$ of dimension $2n$, it was proved by M\o ller and Raussen that the components of the mapping space from $M$ to $S^{2n}$ have exactly two different rational homotopy types. However, since this…
(1) We show that if a presentation of the trivial group is "hard to trivialize", in the sense that lots of Tietze moves are necessary to transform it into the trivial presentation, then the associated presentation complex (which is a…
Whether embedding spaces use all their dimensions equally, i.e., whether they are isotropic, has been a recent subject of discussion. Evidence has been accrued both for and against enforcing isotropy in embedding spaces. In the present…
A topological space is almost locally compact if it contains a dense locally compact subspace. We generalize a result from \cite{Ma}, showing that isomorphism on Borel classes of almost locally compact Polish metric structures is always…
For each finite ordinal n, and each locally-finite group G of cardinality aleph-sub-n, we construct an (n+1)-dimensional, contractible CW-complex on which G acts with finite stabilizers. We use the complex to obtain information about…
Studying crepant blow-ups of (compound) du Val singularities, we classify complexes of coherent sheaves which admit no negative self-extensions -- such a complex, up to flops and mutation equivalences, must either be (1) a module over a…
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…
This paper exhibits a multiplicative and minimal cellular complex which allows explicit and complete (co)homological calculations for the symmetric products of a finite two dimensional CW complex. By considering cohomology, we observe that…
We study the potentially undecidable problem of whether a given 2-dimensional CW complex can be embedded into $\mathbb{R}^4$. We provide operations that preserve embeddability, including joining and cloning of 2-cells, as well as…
We show that if a complex has free finitely generated reduced homology groups for two consecutive dimensions and trivial homology for all other dimensions, then it must have the homotopy type of a wedge of spheres of two consecutive…
The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to…
In this article we prove that every isometric copy of C(L) in C(K) is complemented if L is compact Hausdorff of finite height and K is a compact Hausdorff space satisfying the extension property, i.e., every closed subset of K admits an…
We show how a certain type of CW simplicial resolutions of space by wedges of spheres may be constructed for any topological space, and how such resolutions yield an obstruction theory for a given space X to be a loop space.
Let $X$ be a two-cell complex with attaching map $\alpha\colon S^q\to S^p$, and let $C_X$ be the cofiber of the diagonal inclusion $X\to X\times X$. It is shown that the topological complexity (${\rm TC}$) of $X$ agrees with the…
We present short proofs of Tverberg-type theorems for cell complexes by S. Hasui, D. Kishimoto, M. Takeda, and M. Tsutaya. One of them states that for any prime power $r$, any complex $X$ topologically homeomorphic to $S^{(d+1)(r-1)-1}$,…
We investigate when the categories of all rational $A$-modules and of finite dimensional rational modules are closed under extensions inside the category of $C^*$-modules, where $C^*$ is the cofinite topological completion of $A$. We give a…