Classification of Torus Fibrations Over $S^2$ Up to Fibre Sum Stabilisation

Yibo Zhang

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Classification of Torus Fibrations Over $S^2$ Up to Fibre Sum Stabilisation

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arxiv 2304.09562 v2 pith:LTA2BTRZ submitted 2023-04-19 math.GT math.GR

Yibo Zhang This is my paper

classification math.GTmath.GR

keywords torusfibrationshurwitzlefschetzmonodromiessingularitiestypeadditional

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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 certain torus Lefschetz fibrations. The additional torus Lefschetz fibration is universal when the type of singularities is "simple".

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