Related papers: Every finite complex is the classifying space for …

We prove that every finite connected simplicial complex has the homology of the classifying space for some $\mathrm{CAT}(0)$ cubical duality group. More specifically, for any finite simplicial complex $X$, we construct a locally…

Fiedorowicz suggested that it was likely that every finite simply connected CW complex is homotopy equivalent to the classifying space of a finite semigroup. We prove that every finite wedge of simply connected Moore spaces of finitely…

In this paper we prove that every finite group $G$ can be realized as the group of self-homotopy equivalences of infinitely many elliptic spaces $X$. Moreover, $X$ can be chosen to be the rationalization of an inflexible compact simply…

We show that any action of a finite group on a finitely presentable group arises as the action of the group of self-homotopy equivalences of a space on its fundamental group. In doing so, we prove that any finite connected (abstract)…

We prove that the classifying space of a simplicial group is modeled by its homotopy coherent nerve.

It is an old conjecture, that finite $H$-spaces are homotopy equivalent to manifolds. Here we prove that this conjecture is true for loop spaces. Actually, we show that every quasi finite loop space is equivalent to a stably parallelizable…

For a topological group $G$ let $E_{\textsf{com}}(G)$ be the total space of the universal transitionally commutative principal $G$-bundle as defined by Adem--Cohen--Torres-Giese. So far this space has been most studied in the case of…

Let p be a fibration over a finite simplicial complex, whose fibers have the homotopy type of finite simplicial complexes. Then p is equivalent to an approximate fibration whose total space is a compact ENR. The proof uses homotopy coherent…

Let $X$ be a connected, orientable, 5-dimensional Poincar\'{e} duality complex with torsion-free $H_1(X;\mathbb{Z})$. We show that $\Sigma X$ is homotopy equivalent to a wedge of recognisable spaces and study to what extent its homotopy…

We show that mapping class groups associated to all types of real algebraic curves are virtual duality groups. We also deduce some results about the orbifold homotopy groups of the moduli spaces of real algebraic curves. We achieve these…

In this paper we prove that the quotient of any real or complex moment-angle complex by any closed subgroup in the naturally acting compact torus on it is equivariantly homotopy equivalent to the homotopy colimit of a certain toric diagram.…

Any finite simplicial complex K and a partition of the vertex set of K determines a canonical quotient space of the moment-angle complex of K. We prove that the cohomology groups of such a space can be computed via some Hochster's type…

Let $X$ be an $(n-2)$-connected $2n$-dimensional Poincar\'e complex with torsion-free homology, where $n\geq 4$. We prove that $X$ can be decomposed into a connected sum of two Poincar\'e complexes: one being $(n-1)$-connected, while the…

In this paper we establish a natural definition of Lusternik-Schnirelmann category for simplicial complexes via the well known notion of contiguity. This category has the property of being homotopy invariant under strong equivalences, and…

This paper investigates sufficient and necessary conditions for the existence of a homotopy equivalence between two finite simplicial complexes from an algorithmic point of view. As a result, the conditions are formulated in terms of the…

We answer a weaker version of the classification problem for the homotopy types of $(n-2)$-connected closed orientable $(2n-1)$-manifolds. Let $n\geq 6$ be an even integer, and $X$ be a $(n-2)$-connected finite orientable Poincar\'e…

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.

We propose a generalization of Sullivan's de Rham homotopy theory to non-simply connected spaces. The formulation is such that the real homotopy type of a manifold should be the closed tensor dg-category of flat bundles on it much the same…

We show that the complex of free factors of a free group of rank n > 1 is homotopy equivalent to a wedge of spheres of dimension n-2. We also prove that for n > 1, the complement of (unreduced) Outer space in the free splitting complex is…

Pseudotopological spaces are the Cartesian closed hull of the category of \v{C}ech closure spaces. In this paper, we give a direct proof that the model category of the pseudotopological spaces constructed by Rieser is Quillen equivalent to…