Fundamental Groups in Noncommutative Geometry

Baby NCG Seminar  by Clarisson Canlubo

Abstract: The fundamental group is a powerful and important invariant in topology. Since there are no honest spaces to work with in noncommutative geometry (NCG), the formulation of the fundamental group as the group of homotopy classes of paths does not generalize immediately. In this talk, we will explore another formulation of the fundamental group inspired by the works of Grothendieck in algebraic geometry which lends itself easily to NCG. Afterwards, we will look at the noncommutative analogue of (Galois) covering spaces, known as Hopf-Galois extensions. We will try to give some illustrative examples which shows that in the noncommutative set-up is richer.