The cohomologies of the Iwasawa manifold and of its small deformations

TL;DR

This paper computes the Bott-Chern and Aeppli cohomologies of the Iwasawa manifold and its small deformations, showing these cohomologies are determined by the underlying Lie algebra for certain complex nilmanifolds.

Contribution

It provides explicit cohomology computations for the Iwasawa manifold and its deformations, extending previous results and demonstrating the Lie algebra's role in cohomology determination.

Findings

Cohomologies are determined by the Lie algebra for certain nilmanifolds.

Explicit calculations of Bott-Chern and Aeppli cohomologies for the Iwasawa manifold.

Completes previous partial computations in the literature.

Abstract

We prove that, for some classes of complex nilmanifolds, the Bott-Chern cohomology is completely determined by the Lie algebra associated to the nilmanifold with the induced complex structure. We use these tools to compute the Bott-Chern and Aeppli cohomologies of the Iwasawa manifold and of its small deformations, completing the computations in arXiv:0709.3528v1 [math.AG] by M. Schweitzer.