19 apr 2024 -- 14:30
Geometry in Como (hybrid)
Abstract.
In the context of differentiable manifolds, a relevant role is played by the notion of formality, introduced by Quillen ('69) and Sullivan ('77). A differentiable manifold is said to be formal if its homotopy type (up to torsion) can be recoved by its cohomology ring. A natural cohomological obstruction to formality is given by the existence of non vanishing Massey products, whereas, in the early 00's, Kotschick defined a stronger notion of formality, involving the existence of special Riemannian metrics. In this talk, I will give the main definitions and their interplay, provide the classical examples of (non) formal differentiable manifolds and exhibit the topological obstructions related to formality.