Four-manifolds admitting hyperelliptic broken Lefschetz fibrations

Details Four-manifolds admitting hyperelliptic broken Lefschetz fibrations Four-manifolds admitting hyperelliptic broken Lefschetz fibrations

2011-10-02

arxiv.org/abs/1110.0161v1

Mathematics

Geometric Topology

36 pages, 28 figures

Scientific paper

We introduce hyperelliptic simplified (more generally, directed) broken Lefschetz fibrations, which is a generalization of hyperelliptic Lefschetz fibrations. We construct involutions on the total spaces of such fibrations of genus $g\geq 3$ and extend these involutions to the four-manifolds obtained by blowing up the total spaces. The extended involutions induce double branched coverings over blown up sphere bundles over the sphere. We also show that the regular fiber of such a fibration of genus $g\geq 3$ represents a non-trivial rational homology class of the total space.

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