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arXiv · 2306.15501

The signature of geometrically decomposable aspherical 4-manifolds

Luca Fabrizio Di Cerbo·Marco Golla
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Abstract

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.

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Luca Fabrizio Di Cerbo, Marco Golla. 2023-06-27. The signature of geometrically decomposable aspherical 4-manifolds. https://arxiv.org/abs/2306.15501

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