Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Four-manifolds admitting hyperelliptic broken Lefschetz fibrations   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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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga