Towards Floer theory and Fukaya categories for Generalized Complex Manifolds: Some first ideas

Abstract: Generalized complex (GC) manifolds encompass both symplectic and complex manifolds as examples. From the inception of the field of GC geometry in the early 2000s, questions have thus been raised about its relation to mirror symmetry: Can mirror symmetry be understood as a generalized complex duality, and if so, how? An answer to this general question currently seems out of reach both from the point of view of mirror symmetry, as well as GC geometry -- general GC manifolds are so far relatively poorly understood. However, I have identified a number specific initial questions and approaches which I hope will ultimately help a more general understanding. These ideas -- currently still in their infancy -- are what I would like to outline in this talk.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

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