Postnikov factorizations for shape and proper homotopy theory
by
Luis Javier Hernández
University of La Rioja
Coauthors: J.Ignacio Extremiana, M.Teresa Rivas

We have developed Postnikov sections for Brown-Grossman homotopy groups and for Steenrod homotopy groups in the category of exterior spaces, which is an extension of the proper category. The homotopy fibre of a fibration in the factorization associated with Brown-Grossman groups is an Eilenberg-Mac Lane space for this type of groups, but it has two non-trivial consecutive Steenrod homotopy groups. For a space which is first countable at infinity, one of these groups is given by the inverse limit of the homotopy groups of neighbourhoods at infinity, the other group is isomorphic to the first derived of the inverse limit of this system of groups. In the factorization associated with Steenrod groups the homotopy fibre is an Eilenberg-Mac Lane space for Steenrod groups and it has two non-trivial consecutive Brown-Grossman homotopy groups. Given a compact metric space embedded in the Hilbert cube, its open neighbourhoods provide the Hilbert cube with a structure of exterior space and the homotopy fibres of the factorizations above are Eilenberg-Mac Lane spaces with respect to inward (or approaching) Quigley groups.

Date received: June 24, 2002