Boothby–Wang fibrations on complex contact manifolds

Remarks on Complex Contact Manifolds

1. Statement of results. Let M be a complex manifold of complex dimension 2w + l. Let { Ui} be an open covering of M. We call M a complex contact manifold if the following conditions are satisfied: (1) On each [/,there exists a holomorphic 1-form w,such that Wi/\(do3i)n is different from zero at every point of Ui. (2) If UiC\Uj is nonempty, then there exists a nonvanishing holomorphic function ...

A Note on Homogeneous Complex Contact Manifolds

Duality and Fibrations on G2 Manifolds

We argue that G2 manifolds for M-theory admitting string theory Calabi-Yau duals are fibered by coassociative submanifolds. Dual theories are constructed using the moduli space of M5-brane fibers as target space. Mirror symmetry and various string and M-theory dualities involving G2 manifolds may be incorporated into this framework. To give some examples, we construct two noncompact manifolds w...

Wrinkled Fibrations on Near-Symplectic Manifolds

Motivated by the programmes initiated by Taubes and Perutz, we study the geometry of near-symplectic 4-manifolds and broken Lefschetz fibrations on them. We present a set of four moves which allow us to pass from any given fibration to any other broken fibration which is deformation equivalent to it. The arguments rely on the introduction of a more general class of maps, which we call wrinkled ...

Families of Lagrangian fibrations on hyperkähler manifolds

A holomorphic Lagrangian fibration on a holomorphically symplectic manifold is a holomorphic map with Lagrangian fibers. It is known (due to Huybrechts) that a given compact manifold admits only finitely many holomorphic symplectic structures, up to deformation. We prove that a given compact manifold with b2 > 7 admits only finitely many deformation types of holomorphic Lagrangian fibrations.