Anastasios Papadopoulos: The Eilenberg-MacLane Functor K(1,-) on the Category of Groups

Abstract

In Algebraic Topology one typically tries to study topological spaces by assigning an algebraic structure to them, which is done by defining a functor from a topological category to an algebraic one. Roughly speaking, the goal of my thesis is to do the opposite, that is, to define a functor on the category of groups to a certain topological category with some desired properties. In this talk I will give the basic needed definitions from category theory and briefly introduce some important concepts and results from algebraic topology before outlining the construction of the functor K(1,-).