Topology of fibrations

Abstract

This thesis contains a systematic exposition of the topology of fibrations, including Hurewicz, Dold and Serre fibrations and quasifibrations. The fundamental properties and the classical results due to Hurewicz and Dold are discussed in a detailed way. Many examples illustrate the theory; some of them are used to describe properties peculiar of each class of fibrations. The thesis concludes with a discussion of some recent developments. These are: the functional space studied by P. Booth, P. Heath, C. Morgan and R. Piccinini and its application to fibred exponential laws; the theory of F-spaces and F-fibrations introduced by P. May; a categorical interpretation of a fibration as an algebra over the monad which sends each map to its associated fibration.