On the formality of nearly Kahler manifolds and of Joyce's examples in G_2 holonomy | Sciact - Система учета научной деятельности ИМ СО РАН

On the formality of nearly Kahler manifolds and of Joyce's examples in G_2 holonomy Научная публикация

Журнал

Moscow Mathematical Journal
ISSN: 1609-3321

Вых. Данные

Год: 2024, Том: 24, Номер: 4, Страницы: 495-512 Страниц : 18 DOI: 10.17323/1609-4514-2024-24-4-495-512

Ключевые слова

Nearly Kahler manifold, special holonomy, G2-manifold, Joyce examples, Kummer construction, formality, rational homotopy type, cohomology algebra, intersection homology.

Авторы

Amann Manuel ¹ , Taimanov Iskander A. ²

Организации

1	Institute for Mathematics, Differential Geometry, University of Augsburg, Universit atsstrasse 14, 86159 Augsburg, Germany
2	Sobolev Institute of Mathematics

Информация о финансировании (2)

1	Институт математики им. С.Л. Соболева СО РАН	FWNF-2022-0004
2	Российский фонд фундаментальных исследований	18-01-00411-a

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.

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

Поступила в редакцию:	23 окт. 2023 г.
Принята к публикации:	11 июл. 2024 г.
Опубликована в печати:	4 дек. 2024 г.
Опубликована online:	4 дек. 2024 г.

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

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