Can one classify finite Postnikov pieces?

POSTNIKOV PIECES AND BZ/p-HOMOTOPY THEORY

We present a constructive method to compute the cellularization with respect to BmZ/p for any integer m ≥ 1 of a large class of H-spaces, namely all those which have a finite number of non-trivial BmZ/p-homotopy groups (the pointed mapping space map∗(B m Z/p,X) is a Postnikov piece). We prove in particular that the BmZ/p-cellularization of an H-space having a finite number ofBmZ/p-homotopy grou...

When Can One Finite Monoid Simulate Another?

Relating Postnikov Pieces with the Krull Filtration: a Spin-off of Serre’s Theorem

We characterize H-spaces which are p-torsion Postnikov pieces of finite type by a cohomological property together with a necessary acyclicity condition. When the mod p cohomology of an H-space is finitely generated as an algebra over the Steenrod algebra we prove that its homotopy groups behave like those of a finite complex.

Relating Postnikov pieces with the Krull filtration: a spin-o¤ of Serre’s theorem

We characterize H-spaces which are p-torsion Postnikov pieces of finite type by a cohomological property together with a necessary acyclicity condition. When the mod p cohomology of an H-space is finitely generated as an algebra over the Steenrod algebra we prove that its homotopy groups behave like those of a finite complex. In particular, a p-complete infinite loop space has a finite number o...

Se p 20 04 POSTNIKOV PIECES AND B Z / p - HOMOTOPY THEORY

We present a constructive method to compute the cellularization with respect to B m Z/p for any integer m ≥ 1 of a large class of H-spaces, namely all those which have a finite number of non-trivial B m Z/p-homotopy groups (the pointed mapping space map * (B m Z/p, X) is a Postnikov piece). We prove in particular that the B m Z/p-cellularization of an H-space having a finite number of B m Z/p-h...