On the formality problem for manifolds with special holonomy
Iskander A. Taimanov
TL;DR
This paper surveys the formality problem for manifolds with special holonomy, focusing on recent results regarding Joyce's G_2-manifolds and using intersection Massey products to establish formality.
Contribution
It presents a comprehensive survey and introduces a new approach using intersection Massey products to prove formality of certain special holonomy manifolds.
Findings
Recent results on the formality of Joyce's G_2-manifolds
Application of intersection Massey products to establish formality
Clarification of the formality problem in special holonomy manifolds
Abstract
In sections 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 section 3 we expose the approach to establishing the formality by using the intersection Massey products.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Geometry and complex manifolds