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Classification of torus fibrations over $S^2$ up to fibre sum stabilisation
[Classification des fibrations du tore sur la 2-sphère à stabilisation des sommes de fibres près]
Yibo Zhang1
1Institut Fourier, UMR 5582, Laboratoire de Mathématiques, Université Grenoble Alpes, CS 40700, 38058 Grenoble cedex 9, France
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 1, pp. 137-222

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”.

Nous étudions les fibrations du tore sur la $2$-sphère et l’équivalence de Hurwitz de leurs monodromies. Nous démontrons que, si deux fibrations du tore sur $S^2$ ont le même type de singularités, alors leurs monodromies globales sont équivalentes au sens de Hurwitz après avoir effectué des sommes directes avec une certaine fibration de Lefschetz du tore. Cette fibration de Lefschetz du tore supplémentaire est universelle lorsque le type de singularités est « simple ».

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1843
Classification : 57K20, 57M05, 57K40, 58K10
Keywords: 4-manifold, fibration, monodromy, mapping class group
Mots-clés : variété de dimension 4, fibration, monodromie, groupe de difféotopie

Yibo Zhang  1

1 Institut Fourier, UMR 5582, Laboratoire de Mathématiques, Université Grenoble Alpes, CS 40700, 38058 Grenoble cedex 9, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Classification of torus fibrations over $S^2$ up to fibre sum stabilisation},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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     year = {2026},
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Yibo Zhang. Classification of torus fibrations over $S^2$ up to fibre sum stabilisation. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 35 (2026) no. 1, pp. 137-222. doi: 10.5802/afst.1843

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