Homología efectiva y sucesión espectral de Eilenberg-Moore

Abstract

In this memoir the computability of the effective homology of fibrations is studied. In Chapter 0, the basic notations about effective homology, simplicial sets and computability are introduced. In Chapter 1, an "effective version" of the Eilenberg-Moore spectral sequence is defined. Using this spectral sequence, we give in Chapter 2 an algorithm computing the effective homology of the fiber for a simplicial fibration E? B where B is simply connected and the effective homology of E and B are known. In the last Chapter, by using the above results and the acyclic models method, we find an algorithm computing the effective homology of the simplicial loop space of a simply connected simplicial set whose effective homology is known.