preprint
Inserted: 26 oct 2023
Last Updated: 26 oct 2023
Year: 2022
Abstract:
Exploiting the affinity between stable generalized complex structures and symplectic structures, we explain how certain constructions coming from symplectic geometry can be performed in the generalized complex setting. We introduce generalized Luttinger surgery and generalized Gluck twist along $\mathcal{J}$-symplectic submanifolds. We also export branched coverings to the generalized complex setting. As an application, stable generalized complex structures are produced on a variety of high-dimensional manifolds. Remarkably, some of them have non-homotopy-equivalent path-connected components of their type change locus.