The signature of geometrically decomposable aspherical 4-manifolds

Author:

Luca Fabrizio Di Cerbo, Marco Golla

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Geometric Topology (math.GT)

journal:

date:

2023-06-26 16:00:00

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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