255 citations · 737 across the 27 of their papers we have counts for
22 papers · 1 filter
Non-principal T-duality, generalized complex geometry and blow-ups
Gil R. Cavalcanti, Aldo Witte
We extend the notion of T-duality to manifolds endowed with non-principal torus actions. The singularities of the torus action are controlled by a certain Lie algebroid, called the…
Fibrations in semi-toric and generalized complex geometry
Gil R. Cavalcanti, Ralph L. Klaasse, Aldo Witte
This paper studies the interplay between self-crossing boundary Lefschetz fibrations and generalized complex structures. We show that these fibrations arise from the moment maps in…
Self-crossing stable generalized complex structures
Gil R. Cavalcanti, Ralph L. Klaasse, Aldo Witte
We extend the notion of (smooth) stable generalized complex structures to allow for an anticanonical section with normal self-crossing singularities. This weakening not only allows…
A neighbourhood theorem for submanifolds in generalized complex geometry
Michael Bailey, Gil R. Cavalcanti, Joey van der Leer Duran
We study neighbourhoods of submanifolds in generalized complex geometry. Our first main result provides sufficient criteria for such a submanifold to admit a neighbourhood on which…
Classification of boundary Lefschetz fibrations over the disc
Stefan Behrens, Gil R. Cavalcanti, Ralph L. Klaasse
We show that a four-manifold admits a boundary Lefschetz fibration over the disc if and only if it is diffeomorphic to , $\# m\mathbb{…
Type one generalized Calabi--Yaus
Michael Bailey, Gil R. Cavalcanti, Marco Gualtieri
We study type one generalized complex and generalized Calabi--Yau manifolds. We introduce a cohomology class that obstructs the existence of a globally defined, closed 2-form which…