Strong shape and fibrations

Hanns Thiemann, Frankfurt, Germany

Keywords: strong shape, fibrations, cofibrations, homotopy theory, exponential law AMS Subject classification: Primary: 55P55, 55R99, Secondary: 54C56, 55P05, 55P35, 55Q07

Abstract: We define fibrations and cofibrations in the strong shape category. Various theorems are proved which are well known when continuous maps are considered only. E.g. a long exact sequence for strong shape homotopy groups is deduced. We use cotelescopes to construct a fibre for strong shape morphisms and develop a weak exponential law in the strong shape category.