Bonn Topology Group - Abstracts

General Information - Members - Activities - Topology Seminar

Talk

October 23rd 2018
Falk Beckert (MPIM, Bonn): Higher symmetries on stable homotopy theories.

Abstract

We observe that the combinatorics of the 2-category of parasimplices can be used to define higher variants of Waldhausen's S-construction. From a more representation theoretic perspective the values of these higher S-constructions are related to abstract representations of Iyama's higher Auslander algebras of Dynkin quivers of type A. Using methods from abstract cubical homotopy theory we prove that the parasimplicial combinatoric is stably symmetric. Consequently, we obtain new characterisations of higher S-constructions, as well as a symmetry result for higher Auslander algebras of type A. As a further application, we can lift the construction of higher Toda brackets to a morphism of stable derivators.

Back to seminar page