Classifies torus fibrations over S2 and examines their monodromies, indicating deeper connections in topology.
We study torus fibrations over the 2 -sphere and Hurwitz equivalence of their monodromies. We show that, if two torus fibrations over S 2 have the same type of singularities, then their global monodromies are Hurwitz equivalent after performing direct sums with a certain torus Lefschetz fibration. The additional torus Lefschetz fibration is universal when the type of singularities is “simple”.
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Yibo Zhang (2026) studied this question.