Decoupling Moduli of Configuration Spaces
Moduli and Friends seminar
Monday 19 December 2022
Luciana Basualdo Bonatto (MPIM, Bonn) — Decoupling Moduli of Configuration Spaces
The monoid of oriented surfaces with one boundary component has featured prominently in the works of Miller and Tillmann, and has been essential to Madsen-Weiss' proof of the Mumford conjecture. On another direction, Segal's monoid of configurations in euclidean space originated a branch of scanning results. In this talk, we are going to discuss a combination of these and look at the monoid of moduli of configurations on oriented surfaces. More than being a model for the monoid of punctured surfaces, this approach allows us to look at generalised configuration spaces where particles can have labels and even some collisions are allowed. The moduli of such generalised configuration spaces, defined in the work of Salvatore, have close connections to factorization homology. We will show that the group completion of this monoid of moduli of configurations does not detect that the particles are constrained to the surface: it simply sees surfaces and particles in the infinite euclidean space. In other words, the particles get decoupled and this group completion splits as a product of the well known spaces originated from the surface and Segal's monoids. We will also discuss how similar results can be obtained for configurations in higher dimensional manifolds and also for configuration spaces of submanifolds instead of points.
* Eastern European Time, i.e. UTC+2 in winter and UTC+3 in summer.