On the formality problem for manifolds with special holonomy

Abstract

In \S\S 1 and 2 we follow our online talk at the 21st Geometrical Seminar (Beograd, Serbia) on June 30, 2022 by giving a survey of the formality problem for manifold with special holonomy and exposing recent results by M. Amann and the author on the formality of Joyce's examples of $G_2$-manifolds. In \S 3 we expose the approach to establishing the formality by using intersection Massey products.