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Tamed And Compatible Symplectic Forms On Four-Dimensional Almost Complex Lie Algebras, Andres Cubas

Undergraduate Research at FIU (URFIU) Conference

We are able to give a complete description of four-dimensional Lie algebras g which satisfy the tame-compatible question of Donaldson for all almost complex structures J on g are completely described. As a consequence, examples are given of (non-unimodular) four-dimensional Lie algebras with almost complex structures which are tamed but not compatible with symplectic forms.? Note that Donaldson asked his question for compact four-manifolds. In that context, the problem is still open, but it is believed that any tamed almost complex structure is in fact compatible with a symplectic form. In this presentation, I will define the basic objects involved …