16 sep 2020 -- 16:00
UniPr (online)
Seminari progetto PRIN2017 "Real and Complex Manifolds: Topology, Geometry and Holomorphic Dynamics"
Abstract.
Almost-complex structures are natural generalizations of complex structures and have well known applications in symplectic topology. We will discuss some geometric properties focusing on the closed anti-invariant forms. There exist almost complex 6-manifolds where the space of anti-invariant forms has arbitrarily large dimension, but on 4-manifolds the dimension is conjectured to be related to integrability. We will see explicit examples where perturbing a complex structure to be nonintegrable immediately removes all such forms. This is joint work with Adriano Tomassini and Costantino Medori.