GTA Seminar | Speaker: Sebastián Daza (University of Coimbra)

Title: The holonomy of principal bundle connections over effective orbifolds

Abstract: In this talk we will see how to extend the notion of holonomy group of a connection to effective orbifolds. To do that, first, we will talk about principal orbibundles and a characterization of a class of them in terms of group actions on manifolds. After that, we will talk about connections, horizontal lifts and their relation with the orbifold singularities. Then we will give a definition of the holonomy group, give some ideas of how to proof that it is a Lie group and exhibit its relation with the orbifold structure. If time permits, we will talk about the reduction theorem and the Ambrose-Singer theorem.