Event description
Abstract: The Nijenhuis tensor of an almost complex structure J completely describes when J is integrable. Its image defines a distribution V in the tangent bundle that might be of constant rank. When its rank is constant, V defines a sub-bundle called the torsion bundle, that has nice property especially in dimension 4.
In this talk, we will study the torsion bundle of an almost complex 4-manifold and explore its basic properties. In particular, we will see how to build local frames that describe the torsion bundle and the action of J, and that if the torsion bundle satisfies a certain non-degeneracy condition, then the 4-manifold admits a parallelizable double cover.