Our very own Simone Gutt will restart the geometry seminar after a very long break caused by the COVID pandemic. Her talk is on 09/20/2022, with the title “Almost complex structures, transverse complex structures, and associated Dolbeault cohomologies”. Her abstract is below.
An almost complex structure j on a manifold M is integrable iff its Nijenhuis torsion vanishes iff the +i eigenspace for j is an involutive distribution iff the Dolbeault operator squares to 0. When it is not integrable, various cohomologies have been defined. We are interested here in detecting the existence of a transverse complex structure. The almost complex structure j is maximally non integrable if the image of its Nijenhuis tensor spans the whole tangent bundle TM; those are generic in high dimension. In that case, there is no transverse complex structure and our cohomology vanishes. We suggest a definition of minimally non integrable almost complex structure. This is joint work with Michel Cahen and Jean Gutt.