Resumen de Homotopía propia simplicial I

José Manuel García Calcines , Sergio Rodríguez Machín , Luis Javier Hernández Paricio

• 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.