Homotopía propia simplicial I

  1. García Calcines, José Manuel
  2. Rodríguez Machín, Sergio
  3. Hernández Paricio, Luis Javier
Journal:
Revista de la Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza

ISSN: 0370-3207

Year of publication: 2002

Issue: 57

Pages: 89-112

Type: Article

More publications in: Revista de la Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza

Abstract

The notion of exterior space consists of a topological space together with a certain nonempty family of open subsets that is thought of as a 'system of open neighborhoods at infinity'. An exterior map is a continuous map which is 'continuous at infinity'. In this paper we present and develop the category of exterior spaces as a good framework for proper homotopy theory. As an application we give a new version of the Whitehead theorem for proper homotopy theory. We also give simplicial models for this new category and we analyze singular and realization-type functors for these models.