Postnikov factorizations at infinity
| Autor: | L. Javier Hernández Paricio, M. Teresa Rivas Rodriguez, J. Ignacio Extremiana Aldana |
|---|---|
| Jazyk: | angličtina |
| Předmět: |
Pure mathematics
Homotopy group Homotopy category Homotopy Postnikov system Eilenberg–MacLane space Mathematics::Algebraic Topology Regular homotopy Algebra n-connected Homotopy sphere Brown-Grossman group Mathematics::K-Theory and Homology Mathematics::Category Theory Geometry and Topology Steenrod group Brown–Grossman group Mathematics Postnikov section |
| Zdroj: | RIUR: Repositorio Institucional de la Universidad de La Rioja Universidad de La Rioja (UR) RIUR. Repositorio Institucional de la Universidad de La Rioja instname |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2003.07.022 |
| Popis: | 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 exterior space for this type of groups and 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 the 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 exterior space for this type of groups and it has two non-trivial consecutive Brown-Grossman homotopy groups. We also obtain a mix factorization containing both kinds of previous factorizations and having homotopy fibres which are Eilenberg-Mac Lane exterior spaces for both kinds of groups. Given a compact metric space embedded in the Hilbert cube, its open neighbourhoods provide the Hilbert cube the structure of an exterior space and the homotopy fibres of the factorizations above are Eilenberg-Mac Lane exterior spaces with respect to inward (or approaching) Quigley groups. © 2004 Elsevier B.V. All rights reserved. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|