Bonn Topology Group - Abstracts

General Information - Members - Activities - Topology Seminar

Talk

June 23rd 2020
Vincent Braunack-Mayer (New York University Abu Dhabi): Modules, comodules, and rational homotopy theory

Abstract

In the late 60's, Quillen proved that the rational homotopy theory of simply-connected spaces is completely encoded by differential graded Lie algebras and by differential graded coalgebras over the rationals. I will explain how to extend this correspondence to representation categories, identifying fibrewise rational stable homotopy over simply-connected spaces with Lie representations and comodules. This is the basis of a rich dictionary relating algebraic constructions (ext groups, cotor functors) with topology (stable section spaces, fibrewise smash products), various aspects of which I will explain. Time permitting, I will also discuss a dual approach based on Sullivan's rational homotopy theory that captures nilpotent fundamental group actions.

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