Description:

Title: Local fundamental groups of log canonical singularities of low dimension

Abstract: In this talk, we will define the local fundamental group of an isolated singularity as the fundamental group of its link. For algebraic singularities, Kapovich and Kollár showed that any finitely presented group can appear. Although, restrictions appear if one restricts to different families of singularities. For the case of log canonical singularities, we will show that in dimension 3 the free groups cannot appear. Finally, we will present a construction for some local fundamental groups in dimensions 3 and 4. This construction, in particular, will yield the free groups as the local fundamental group of isolated 4-dimensional log canonical singularities.
This is based on joint work with Joaquín Moraga