Aspherical 4-Manifolds, Complex Structures, and Einstein Metrics
Differential Geometry
2024-04-22 v4 Geometric Topology
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.
Cite
@article{arxiv.2303.13219,
title = {Aspherical 4-Manifolds, Complex Structures, and Einstein Metrics},
author = {Michael Albanese and Luca F. Di Cerbo},
journal= {arXiv preprint arXiv:2303.13219},
year = {2024}
}
Comments
A typo in the proof of Theorem 1 is corrected. 10 pages, no figures. To appear in J. Geometric Analysis