The Dutch Differential Topology & Geometry seminar (DDT&G)

Speaker: Leopold Zoller

Title: Massey Products and formal domination

Abstract: The singular cochain algebra of a space contains a lot of information beyond the cohomology algebra. A key technique in rational homotopy theory is to replace the singular cochains by smaller models in order to make that information visible. In the first talk, we will give an example driven introduction to some techniques from rational homotopy theory such as Sullivan models of spaces. These will then be used to study certain higher operations on the cohomology algebra called Massey products. In particular we will encounter formal spaces, which can be understood as those spaces with vanishing higher operations. 

In the second talk we will study the behaviour of Massey products under the relation of domination: if there is a map of nonzero degree between two compact manifolds, then we say that the source dominates the target. There is a general heuristic in geometry that the dominated manifold is “simpler” than the source. We show that this turns out to be true in the realm of rational homotopy theory when interpreting simplicity as the vanishing of higher operations. This is based on joint work with Jonas Stelzig and Aleksandar Milivojevic.