Seminar in Real and Complex Geometry

Thursday, March 14, 2019, 16:00-18:00, Schreiber building, room 209

Aziz Kharoof (Haifa University)

Higher order Toda brackets


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 the construction will be explained using simple examples for chain complexes.