Nonabelian Algebraic Topology : filtered spaces , crossed complexes ,

Nonabelian Algebraic Topology : filtered spaces , crossed complexes , cubical higher homotopy groupoids

Se p 20 04 Postnikov Invariants of Crossed Complexes

We determine the Postnikov Tower and Postnikov Invariants of a Crossed Complex in a purely algebraic way. Using the fact that Crossed Complexes are homotopy types for filtered spaces, we use the above " algebraically defined " Postnikov tower and Postnikov invariants to obtain from them those of filtered spaces. We argue that a similar " purely algebraic " approach to Postnikov invariants may a...

Postnikov invariants of crossed complexes

We determine the Postnikov tower and Postnikov invariants of a crossed complex in a purely algebraic way. Using the fact that crossed complexes are homotopy types for filtered spaces, we use the above “algebraically defined” Postnikov tower and Postnikov invariants to obtain from them those of filtered spaces. We argue that a similar “purely algebraic” approach to Postnikov invariants may also ...

Exact Sequences of Fibrations of Crossed Complexes, Homotopy Classification of Maps, and Nonabelian Extensions of Groups

The classifying space of a crossed complex generalises the construction of Eilenberg-Mac Lane spaces. We show how the theory of fibrations of crossed complexes allows the analysis of homotopy classes of maps from a free crossed complex to such a classifying space. This gives results on the homotopy classification of maps from a CW -complex to the classifying space of a crossed module and also, ...

Triadic van Kampen and Hurewicz Theorems∗

In [BH5] it is shown how the Relative Hurewicz Theorem follows from a Generalised Van Kampen Theorem (GVKT) for the fundamental crossed complex of a filtered space, and in [BL3] it is shown how a new multirelative Hurewicz Theorem follows from a GVKT for the fundamental cat-group of an n-cube of spaces. The purpose of this paper is to advertise and explain some implications and special cases of...