English

Every 4-Manifold is BLF

Geometric Topology 2009-01-07 v4 Algebraic Geometry

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).

Keywords

Cite

@article{arxiv.0803.2297,
  title  = {Every 4-Manifold is BLF},
  author = {Selman Akbulut and Cagri Karakurt},
  journal= {arXiv preprint arXiv:0803.2297},
  year   = {2009}
}

Comments

24 pages, 14 figures, published version

R2 v1 2026-06-21T10:21:50.481Z