K. Borsuk in 1979, at the Topological Conference in Moscow, introduced concept of the capacity of a compactum and asked some questions concerning properties of the capacity ofcompacta. In this paper, we give partial positive answers to three of these questions in some cases. In fact, by describing spaces homotopy dominated by Moore and Eilenberg-MacLane spaces, the capacities of a Moore space $...

This paper is the second one in a series of papers about operations in motivic cohomology. Here we show that in the context of smooth schemes over a field of characteristic zero all the bi-stable operations can be obtained in the usual way from the motivic reduced powers and the Bockstein homomorphism (Theorem 4.46). This paper has been delayed for many years because I tried to find a way to ex...

Let A be a simplicial bicommutative Hopf algebra over the field F2 with the property that π0A ∼= F2. We show that π∗A is a functor of the André-Quillen homology of A, where A is regarded as an F2 algebra. Then we give a method for calculating that André-Quillen homology independent of knowledge of π∗A. Let G be an abelian group. Since the work of Serre [19] and Cartan [6], we have know that the...

We calculate the RO(G)-graded coefficients of HZ_, Eilenberg-MacLane spectrum constant Mackey functor for quaternion group Q8.

Generalising Segal’s approach to 1-fold loop spaces, the homotopy theory of n-fold loop spaces is shown to be equivalent to the homotopy theory of reduced Θn-spaces, where Θn is an iterated wreath-product of the simplex category ∆. A sequence of functors from Θn to Γ allows for an alternative description of the Segal-spectrum associated to a Γ-space. In particular, each Eilenberg-MacLane space ...

The braid group of n-strings is the group of homotopy types of movements of n distinct points in the 2-plane R. It was introduced by E. Artin [1] in 1926 in order to study knots in R. He gave a presentation of the braid group by generators and relations, which are, nowadays, called the Artin braid relations. Since then, not only in the study of knots, the braid groups appear in several contexts...

We describe the effect of homological plus-constructions on the homotopy groups of Eilenberg-MacLane spaces in terms of universal central extensions.