An Axiomatic Approach to the Hurewicz Theorem for Symmetric Spectra

Abstract

Two important invariants in classical algebraic topology are the homotopy groups and the homology groups. The first of these are notoriously difficult to compute while the second is reasonably easier. The Hurewicz homomorphism is a natural transformation between these invariants which can make computation of some homotopy groups easier. In this thesis we will look at the analogue of these invariants, and of the Hurewicz homomorphism, for the category of interest in modern stable homotopy theory.