Joel Fredin: Interactions Between Covering Spaces and Fundamental Groupoids

Abstract

In this talk, we will study the relationship between the category of sets equipped with an action by the fundamental groupoid of a topological space X and the category of covering spaces over X. We will see, through construction of functors, that these categories are more or less the same by showing that they are equivalent as categories. We then proceed by considering reconstruction problems. This seeks to understand whether it is possible to reconstruct the group if we know the automorphism group of a certain functor behaves. We will then use that theory to relate the topological fundamental group to an algebreo-geometric one.

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