28 mar 2019 -- 14:30
Sala Seminari, DM, Pisa
Abstract.
In this talk we will introduce the ordered and unordered configuration spaces of a manifold. Our aim is to give an overview of the main classical results and then we focus on the Betti numbers in the case of surfaces.
The main idea behind the aforementioned results is considering all these spaces simultaneously. The natural maps - that consist in adding or removing a point - will be described. Also inclusions between manifolds give remarkable properties. In the second part we will describe the Kriz model for rational homotopy type of configuration spaces. Using that model and some representation theory, we will compute the Betti and Hodge numbers of the unordered configuration spaces of surfaces.
I soli prerequisiti per seguire questo seminario sono: topologia di base (corso di geometria 2) e la conoscenza di almeno una teoria coomologica (quanto è stato fatto finora al corso di elementi di topologia algebrica è sufficiente).