What question did this study set out to answer?

The main aim is to explore the relationship between torus fibrations over S2 and Hurwitz equivalence of their monodromies.

January 14, 2026Annales de la faculté des sciences de Toulouse Mathématiques0 citationsOpen Access

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Classification of torus fibrations over S 2 up to fibre sum stabilisation

YZYibo ZhangLaboratoire de Mathématiques

Key Points

The main aim is to explore the relationship between torus fibrations over S2 and Hurwitz equivalence of their monodromies.
Analyzing torus fibrations over the 2-sphere
Investigating types of singularities for the fibrations
Using direct sums with a torus Lefschetz fibration for equivalence checks
Finds that torus fibrations with the same singularities have Hurwitz equivalent monodromies
Demonstrates universality of the additional Lefschetz fibration when singularities are simple

Abstract

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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Classification of torus fibrations over S 2 up to fibre sum stabilisation

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