Aspherical 4-manifolds and (almost) complex structures

Geometry Topology Seminar
Friday, March 17, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Luca Di Cerbo – University of Florida –
Igor Belegradek

A well-known conjecture of Dennis Sullivan asserts that a hyperbolic n-manifold with n>2 cannot admit a complex structure. This conjecture is known to be true in dimension four but little is known in higher dimensions. 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 positive Euler number cannot support a complex structure.  This is joint work with M. Albanese.