Fibrations over Topological Groups

Abstract

This thesis serves three purposes. First, we define Wu classes of representations and compute them for orthogonal representations of cyclic groups. Next, we provide an exposition to simplicial homotopy theory and discuss some pivotal constructions such as the Kan Loop Functor. We show how to recover a topological group from its classifying space up to homotopy equivalence. Finally, we provide partial results in the characterization of principal fibrations with fiber an Eilenberg-MacLane space.