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Pré-Publication, Document De Travail Année : 2023

The signature of geometrically decomposable aspherical 4-manifolds

Résumé

We construct examples of geometrically decomposable aspherical 4-manifolds with non-zero signature. We show that all such 4-manifolds satisfy the inequality (of Bogomolov--Miyaoka--Yau type) $\chi\geq 3|\sigma|$. We also construct examples attaining the equality that are non-geometric and have non-zero signature. Finally, we prove that for higher graph 4-manifolds, with complex-hyperbolic vertices, the strict inequality always holds. Moreover, we construct infinitely many examples of higher graph 4-manifolds with non-zero signature and prove that the inequality is strict and sharp in this class.

Dates et versions

hal-04266692 , version 1 (31-10-2023)

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Luca Fabrizio Di Cerbo, Marco Golla. The signature of geometrically decomposable aspherical 4-manifolds. 2023. ⟨hal-04266692⟩

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