Every 4-Manifold is BLF

Details Every 4-Manifold is BLF Every 4-Manifold is BLF

2008-03-15

arxiv.org/abs/0803.2297v4

Journal of Gokova Geometry Topology, Volume 2 (2008) 83-106

Mathematics

Geometric Topology

24 pages, 14 figures, published version

Scientific paper

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).

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