Leopold Zoller: Domination preserves formality

Abstract.

If there is a map of nonzero degree between orientable compact manifolds, then we say that the source dominates the target. According to a general heuristic, in this case the dominated manifold is "simpler" (or equal) than the source. From the point of view of rational homotopy theory, formal spaces are in a sense the simplest spaces with a given cohomology ring. We show that the heuristic actually holds in the sense that formality is preserved under domination and investigate subtleties with respect to the vanishing of Massey products. This is joint work with Aleksandar Milivojevic and Jonas Stelzig.