On the topological proof of the Mumford conjecture

Abstract

This dissertation is a introductory monograph on the topological viewpoint of Mumford’s conjecture. The first part studies the homotopy theoretical tools of infinite loop spaces, the Group Completion Theorem and the plus construction. The second part is a survey about the development of the problem from the original formulation of the conjecture to the Generalized Madsen-Weiss Theorem and its proof.