Every 4-Manifold is BLF
arXiv:0803.2297
Abstract
Here we show that every compact smooth 4-manifold X has a structure of a Broken Lefschetz Fibration (BLF in short). Furthermore, if b_{2}^{+}(X)> 0 then it also has a Broken Lefschetz Pencil structure (BLP) with nonempty base locus. This imroves a Theorem of Auroux, Donaldson and Katzarkov, and our proof is topological (i.e. uses 4-dimensional handlebody theory).
24 pages, 14 figures, published version
References in corpus (7)
- A Legendrian surgery presentation of contact 3-manifolds
- Singular Lefschetz pencils
- Wrinkled fibrations on near-symplectic manifolds
- Constructing Lefschetz-type fibrations on four-manifolds
- Constructing symplectic forms on 4-manifolds which vanish on circles
- Topology of broken Lefschetz fibrations and near-symplectic 4-manifolds
- An open book decomposition compatible with rational contact surgery
Cited by in corpus (10)
- Wrinkled fibrations on near-symplectic manifolds
- Poisson structures on smooth 4-manifolds
- Geometric structures and Lie algebroids
- Modification rule of monodromies in R_2-move
- Braiding link cobordisms and non-ribbon surfaces
- Fibrations in semi-toric and generalized complex geometry
- Handlebody argument for modifying achiral Lefschetz singularities
- The Kodaira Dimension of Lefschetz Fibrations
- Generic fibrations around multiple fibers
- Bordered Floer Homology and Lefschetz fibrations with corners