ETD

• algebraic
• configuration space
• homotopy
• topology

In the thesis we present a general investigation on the homotopy invariance property of configuration spaces. Initially, we present the counter example of Longoni and Salvatore, who prove that configuration spaces are not an homotopy invariant for closed manifold. They exhibit a non-simply-connected counterexample using lens spaces. The question now become: are configuration spaces homotopy invariants for simply connected closed manifold? In the second chapter we give all the necessary techniques (algebraic and homotopic) of CDGA and Model category, to prove the theorem of Najib Idrissi. It states that in fact there is a property of real homotopy invariance. Then we do a little survey around the question and present some positive results of the literature. We then proceed - as a lateral biproduct - to give some little novel results about betti numbers of configuration spaces of the projective quaternionic plane and some explicit generating cocycles.