Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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L. Sillari

Generalized Luttinger surgery and other cut-and-paste constructions in generalized complex geometry

created by sillari on 26 Oct 2023



Inserted: 26 oct 2023
Last Updated: 26 oct 2023

Year: 2022

ArXiv: 2208.00534 PDF


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.

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