Aspherical 4-Manifolds, Complex Structures, and Einstein Metrics

Michael Albanese; Luca F. Di Cerbo

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arXiv · 2303.13219

Aspherical 4-Manifolds, Complex Structures, and Einstein Metrics

Michael Albanese·Luca F. Di Cerbo

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Abstract

We show that extended graph 4-manifolds with positive Euler characteristic cannot support a complex structure. This result stems from a new proof of the fact that a closed real-hyperbolic 4-manifold cannot support a complex structure. Finally, we construct infinitely many extended graph 4-manifolds with positive Euler characteristic which support almost complex structures.

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Michael Albanese, Luca F. Di Cerbo. 2023-03-23. Aspherical 4-Manifolds, Complex Structures, and Einstein Metrics. https://arxiv.org/abs/2303.13219

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