Formality and geometric structures

Abstract

In this thesis we discuss the notion of formality, a topological property allowing calculations of the rational homotopy groups from the cohomology algebra. We discuss the algebraic theory, together with the connections between formality and geometric structures, showing that symmetric spaces, Kähler manifolds and quaternionic Kähler manifolds are formal, and presenting new results on formality in combination with Mayer-Vietoris in the context of G2-manifolds.