Online: Orr's homotopy invariants for Galois groups

Zoom Online Meeting ID: 919 6497 4060
For password see the email or contact Pieter Moree (moree@mpim...).

In the study of Galois action on étale fundamental groups of algebraic curves, one approach is to consider an analogy between absolute Galoisgroups and mapping class groups of surfaces as in Ihara's initial work of such representation.

In this talk, based on such analogy, we introduce and study the arithmetic analogue of Orr's homotopy invariants in knot theory. Orr's homotopy invariants are defined for based links and valued in the third homotopygroup of some space obtained from the Eilenberg-MacLane space of a freenilpotent group. We construct the analogous object via the techniques of profinite completion of CW complexes by Artin-Mazur, Friedlander and Sullivan. Moreover, as an application, we compare the arithmetic analogue of Orr's invariants and Ellenberg's obstruction class to homotopy sections in the context of Grothendieck section conjecture. This is joint work with Yuji Terashima.