Thursday 10 Nov 2016: The logarithmic point is an Eilenberg-MacLane space
Valentina Di Proietto - University of Exeter
A classical Eilenberg-MacLane space is a topological space for which the fundamental group is the only non-vanishing homotopy group. In this talk we translate the notion of Eilenberg-MacLane space in the context of algebraic varieties. The fundamental group defined in terms of homotopy classes of loops does not work in this context, but generalizing the Riemann-Hilbert correspondence we can define a fundamental group which works in very general frameworks. We will show that the logarithmic point is an Eilenberg-MacLane space in this new sense, and we show how this is related to the existence of a homotopy exact sequence of a fibration where the logarithmic point is the base. This is a joint work with Atsushi Shiho.