Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations

Details Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations Noncomplex smooth 4-manifolds with genus-2 Lefschetz fibrations

1998-10-01

arxiv.org/abs/math/9810007v2

Proc. Amer. Math. Soc. 128 (2000), 3125-3128

Mathematics

Geometric Topology

Scientific paper

We construct noncomplex smooth 4-manifolds which admit genus-2 Lefschetz
fibrations over S^2. The fibrations are necessarily hyperelliptic, and the
resulting 4-manifolds are not even homotopy equivalent to complex surfaces.
Furthermore, these examples show that fiber sums of holomorphic Lefschetz
fibrations do not necessarily admit complex structures.

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