Acyclic Classes of Nonrepresentable Homologies

Abstract

A homology theory is a collection of functors that assign to each topological space a collection of abelian groups and satisfy certain axioms. Since one of these axioms is homotopy invariance, homology theories are useful tools to study the homotopy type of spaces. This project is focused on homology theories defined over CW-complexes, as customary. Most of the authors restrict to a smaller class of homology theories: the representable homology theories. Representable homology theories have many nice properties, one of which is that they commute with directed colimits.