In this monograph we give an exposition of some recent development in homotopy theory. It
relates to advances in periodicity in homotopy localization and in cellular spaces. The notion …

For a two-dimensional Moore space M with fundamental group G, we identify the effect of the
cellularization CW M and the fibre\overline P _M of the nullification on an Eilenberg—Mac …

We examine different constructions for the join of two topological spaces, simplicial sets and
small categories. We give a systematic account of this and try to clarify the interrelations …

We show that cellular approximations of nilpotent Postnikov stages are always nilpotent
Postnikov stages, in particular classifying spaces of nilpotent groups are turned into …

The way spaces are often studied in homotopy theory is by decomposing and approximating
them using simpler and possibly better understood pieces. This is typically done in two …

We establish sufficient conditions for the nerve of the centric linking system of ap-local finite
group (S, ℱ, ℒ) to have the homotopy type of an Eilenberg-MacLane space K (Γ, 1) for a …

There is a classical" duality" between homotopy and homology groups in that homotopy
groups are compatible with homotopy pullbacks (every homotopy pullback gives rise to a …

We introduce Clapp-Puppe type generalized Lusternik-Schnirelmann (co) category in a
Quillen model category. We establish some of their basic properties and give various …

We describe the projectives in the category of functors from a DCC poset to abelian groups.
Based on this description we define a related condition, pseudo-projectivity, and we prove …