For any countable CW -complex K and a cardinal number τ ≥ ω we construct a completely metrizable space X(K, τ) of weight τ with the following properties: e-dimX(K, τ) ≤ K, X(K, τ) is an absolute extensor for all normal spaces Y with e-dimY ≤ K, and for any completely metrizable space Z of weight ≤ τ and e-dimZ ≤ K the set of closed embeddings Z → X(K, τ) is dense in the space C(Z,X(K, τ)) of al...

A self-map f on the CW complex Z is a periodic homotopy idempotent if for some r 0 and p > 0 the iterates fr and fr+p are homotopic. Geoghegan and Nicas defined the rotation index RI(f) of such a map. They proved that for r = p = 1, the homotopy idempotent f splits if and only if RI(f) = 1, while for r = 0, the index RI(f) divides p2. We extend this to arbitrary p and r, and generalize various ...

This paper proves a conjecture of Fomin and Shapiro that their combinatorial model for any Bruhat interval for any finite Weyl group is a regular CW complex which is homeomorphic to a ball. The model consists of a stratified space which may be regarded as the link of an open cell in a larger closed cell, all within the totally nonnegative part of the unipotent radical of an algebraic group. A k...

We prove that every amenable group of cohomological dimension two whose integral ring is a domain solvable and investigate certain homological finiteness properties groups satisfy the analytic zero divisor conjecture act on an acyclic CW-complex with stabilisers.

The paper is devoted to investigation of some properties of [L]-homotopy groups. It is proved, in particular, that for any finite CW -complex L, satisfying double inequality [S] < [L] ≤ [S], π [L] n (S) = Z. Here [L] denotes extension type of complex L and π [L] n (X) denotes n-th [L]-homotopy group of X .

For each Artin group we compute the reduced `cohomology of (the universal cover of) its “Salvetti complex”. This is a CW-complex which is conjectured to be a model for the classifying space of the Artin group. In the many cases when this conjecture is known to hold our calculation describes the reduced `-cohomology of the Artin group.

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...

Given any group Γ, there is an aspherical CW -complex BΓ (also denoted by K(Γ, 1)) with fundamental group Γ; moreover, BΓ is unique up to homotopy equivalence (cf. [Hu]). BΓ is called the classifying space of Γ. (BΓ is also called an Eilenberg-MacLane space for Γ.) So, the theory of aspherical CW -complexes, up to homotopy, is identical with the theory of groups. This point of view led to the n...

Associated to every finite simplicial complex K there is a “moment-angle” finite CW-complex, ZK ; if K is a triangulation of a sphere, ZK is a smooth, compact manifold. Building on work of Buchstaber, Panov, and Baskakov, we study the cohomology ring, the homotopy groups, and the triple Massey products of a moment-angle complex, relating these topological invariants to the algebraic combinatori...

The associations of HLA-B*4402 and HLA-B*4403 with alleles of HLA-A and HLA-Cw were investigated in panels of HLA-B*4403 and HLA-B*4402 homozygous individuals and in selected individuals carrying HLA-Cw*04 and HLA-B*4403. Some of these individuals were genotyped and also carried (HLA-DRB1*0701, DQB1*02). Among the latter, we studied individuals carrying the conserved extended haplotype (CEH) [H...