Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Diffeomorphism Groups and Moduli of Configuration Spaces via Homological Stability

In this talk, we will discuss recent advances into the study of diffeomorphism groups of manifolds using techniques such as homological stability. This comes from the point of view of studying the classifying spaces of diffeomorphism groups as a tool to understand their group structure, topology and also invariants such as characteristic classes of smooth bundles. I will start by recalling this approach and discuss how it has been successful by presenting some recent insights and developments in the area. Moreover, I will discuss how such techniques give us splitting results in the context of manifolds with punctures and how these spaces are closely related to moduli of configuration spaces. Finally, I will show how these results generalise to more sophisticated spaces such as moduli of configurations with partially summable labels, where some collisions of particles are allowed, which is deeply related to factorisation homology.