Institut de Mathématiques de Marseille, UMR 7373


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Branched covering over the sphere

Lundi 11 septembre 2017 14:00-15:00 - Natalia VIANA - I2M, Marseille

Branched covering over the sphere

Résumé : A branched covering of degree d over the sphere determines a finite collection D of partitions of d, called the branch datum. The converse of this assertion is not true. In 1984, A. Edmonds, R. Kulkarni and R. Stong exhibit, for any non-prime integer d, an exceptional collection, i.e. a collection of partitions satisfying the necessary conditions but that is not realizable as a branch datum of any branched covering over S^2.
This realization problem is still open. It was completely solved just for collections involving a "short" partition like :
1. [d], by R. Thom in 1965, via complex polynomials ;
2. [d-1,1], by A. Edmonds, R. Kulkarni and R. Stong in 1984, via permutation groups ;
3. [d-2,2], by E. Pervova and C. Petronio in 2008, via minimal checker-board graphs.
For other collections are known, at most, partial results.
In this talk, I would like to introduce the problem and some of the techniques used to study it.

Lieu : CMI, salle de séminaire R164 (1er étage) - I2M - Château-Gombert
39 rue Frédéric Joliot-Curie
13453 Marseille cedex 13

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Pour en savoir plus sur cet événement, consultez l'article Séminaire Géométrie, Dynamique et Topologie (GDT)