Abstract: It is a prominent conjecture (relating Riemannian geometry and algebraic topology) that all simply-connected compact manifolds of special holonomy should be formal spaces, i.e., their rational homotopy type should be derivable from their rational cohomology algebra already — an as prominent as particular property in rational ho-motopy theory. Special interest now lies on exceptional holonomy G2 and Spin(7). In this article we provide a method of how to confirm that the famous Joyce examples of holonomy G2 indeed are formal spaces; we concretely exert this computation for one example, which may serve as a blueprint for the remaining Joyce examples (potentially also of holonomy Spin(7)). These considerations are preceded by another result identifying the formality of manifolds admitting special structures: we prove the formality of nearly Kähler manifolds. A connection between these two results can be found in the fact that both “special holonomy” and “nearly Kähler” naturally generalize compact Kähler manifolds, whose formality is a classical and celebrated theorem by Deligne–Griffiths–Morgan–Sullivan. © 2024 Independent University of Moscow.

Cite: Amann M. , Taimanov I.A.
On the formality of nearly Kahler manifolds and of Joyce's examples in G_2 holonomy
Moscow Mathematical Journal. 2024. V.24. N4. P.495-512. DOI: 10.17323/1609-4514-2024-24-4-495-512 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Oct 23, 2023
Accepted:	Jul 11, 2024
Published print:	Dec 4, 2024
Published online:	Dec 4, 2024

Identifiers:

Web of science:	WOS:001417123900001
Scopus:	2-s2.0-85210441883
Elibrary:	78946230
OpenAlex:	W3114155621

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