Michael Albanese

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math.DG2025

Hodge theoretic results for nearly Kähler manifolds in all dimensions

Michael Albanese, Spiro Karigiannis, Lucía Martín-Merchán +1

We generalize to nearly Kähler manifolds of arbitrary dimensions most of the Hodge-theoretic results for nearly Kähler $6$ -manifolds that were established by Verbitsky. In particul…

math.DG2024

Generalized almost-Kähler-Ricci solitons

Michael Albanese, Giuseppe Barbaro, Mehdi Lejmi

We generalize Kähler-Ricci solitons to the almost-Kähler setting as the zeros of Inoue's moment map \cite{MR4017922}, and show that their existence is an obstruction to the existen…

math.DG2023

Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-Lück Inequality $χ \geq ∣ σ ∣$

Michael Albanese, Luca F. Di Cerbo, Luigi Lombardi

We discuss the Singer conjecture and Gromov-Lück inequality $χ \geq ∣ σ ∣$ for aspherical complex surfaces. We give a proof of the Singer conjecture for aspherical complex surface wit…

Hodge theoretic results for nearly Kähler manifolds in all dimensions

Generalized almost-Kähler-Ricci solitons

Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-Lück Inequality χ≥∣σ∣

Aspherical Complex Surfaces, the Singer Conjecture, and Gromov-Lück Inequality $χ \geq ∣ σ ∣$