Dolbeault formality for complex nilmanifolds
Differential Geometry
2026-02-17 v1 Algebraic Topology
Abstract
A quasi-isomorphism of differential graded algebras (DGA) is a multiplicative map inducing an isomorphism on cohomology. A DGA is called formal if it can be connected by a chain of quasi-isomorphisms to its cohomology algebra. We prove that the Dolbeault DGA of a complex nilmanifold is formal only if it is a torus, and the Dolbeault algebra of (0,p)-forms is formal if and only if the complex structure is abelian.
Cite
@article{arxiv.2602.13426,
title = {Dolbeault formality for complex nilmanifolds},
author = {Tommaso Sferruzza and Misha Verbitsky},
journal= {arXiv preprint arXiv:2602.13426},
year = {2026}
}
Comments
15 pages, v. 1.0