Thursday November 7th, 2019
Time: 4:00 PM - 5:00 PM
Title: New techniques for studying the topology and geometry of almost complex manifolds.
Speaker: Scott Wilson, Queen's College
Location: Math Tower P-131
There is a fascinating interplay in the topology and geometry of manifolds among the various tensors one can consider such as non-degenerate bilinear forms and almost complex structures. Each of these are informed by a certain flatness or integrability condition, and have been studied to varying degrees of success.
In this talk, I'll focus on the lattermost category, describing a new sequence of cohomology groups that can be defined in the context of almost complex manifolds, which generalizes a well-studied object in the theory of complex manifolds. This will be defined by very elementary means, and some interesting examples will be computed, which show there is a rich theory to be explored involving both topology and geometry. As I'll explain, in dimension 6 the groups can be used to prohibit the existence of an interesting class of compatible metrics, the so-called nearly Kahler metrics, which adds to this fascinating interplay.