Compact holonomy G2 manifolds need not be formal

Martín-Merchán, Lucía

doi:10.2140/gt.2026.30.1109

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author index

To appear

Other MSP journals

Compact holonomy $G_2$ manifolds need not be formal

Lucía Martín-Merchán

Geometry & Topology 30 (2026) 1109–1127

DOI: 10.2140/gt.2026.30.1109

Abstract

We construct a compact simply connected manifold with holonomy $G_{2}$ that is nonformal. This manifold is the resolution of a flat $G_{2}$ orbifold with $ℤ_{2}$ isotropy, which can be resolved using both the generalized Kummer construction by D. D. Joyce and the method developed by Joyce and S. Karigiannis. A nonvanishing triple Massey product is obtained by arranging the singular locus in a particular configuration.

Keywords

holonomy $\mathrm{G}_2$ manifolds, formality, Massey products

Mathematical Subject Classification

Primary: 53C29, 55P62, 55S30

References

Publication

Received: 4 November 2024

Revised: 6 April 2025

Accepted: 29 August 2025

Published: 20 April 2026

Proposed: Simon Donaldson

Seconded: Nathalie Wahl, Aaron Naber

Authors

Lucía Martín-Merchán
Institut für Mathematik Humboldt Universität zu Berlin Berlin Germany

Open Access made possible by participating institutions via Subscribe to Open.

Volume 30, issue 3 (2026)