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arXiv · 2602.13426

Dolbeault formality for complex nilmanifolds

Tommaso Sferruzza·Misha Verbitsky
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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.

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Tommaso Sferruzza, Misha Verbitsky. 2026-02-13. Dolbeault formality for complex nilmanifolds. https://arxiv.org/abs/2602.13426

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