Higher order Toda brackets

Abstract: Toda brackets are a type of higher homotopy operation. Like Massey products, they are not always defined, and their value is indeterminate. Nevertheless, they play an important role in algebraic topology and related fields: Toda originally constructed them as a tool for computing homotopy groups of spheres. Adams later showed that they can be used to calculate differentials in spectral sequences.

After reviewing the construction and properties of the classical Toda bracket, we shall describe a higher order version, there are two ways to do that. We will provide a diagrammatic description for the system we need to define the higher order Toda brackets, then we will use that to give alternative definition using the homotopy cofiber.

algebraic topologycategory theorygroup theoryK-theory and homology

Audience: researchers in the topic

Cihan Okay

Series comments: Contact the organizer to get access to Zoom.

Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos