Classification of metric fibration

Abstract

In this talk, we explain the classificatin of the metric fibration that is a metric analogue of topological fibration introduced by T. Leinster in the study of magnitude. The magnitude of metric spaces, also introduced by Leinster, is an analogy of the Euler characteristic from a viewpoint of enriched category theory. As the Euler characteristic of the usual fibration splits into those of the base and the fiber, the magnitude has the same property with respect to the metric fibration. The classification goes pararell to the topological case, namely it's reduced to that of the principal G fibration, however, we need to consider a group G as a group object in the category of metric spaces. We start the talk from an introduction to magnitude theory.