Complex structures on 4-manifolds

Luca Di Cerbo, University of Florida

A well-known conjecture of Dennis Sullivan (Abel Prize 2022) asserts that a hyperbolic n-manifold cannot admit a complex structure. This conjecture is known to be true in dimension four (Toledo, Carlson, LeBrun). In this talk, I will outline a new proof of the fact that a hyperbolic 4-manifold cannot support a complex structure. This new proof has some nice features, and it generalizes to show that all extended graph 4-manifolds with at least one pure real-hyperbolic piece cannot support a complex structure.  This is joint work with M. Albanese.

MC 5417