Branched covering over the sphere
Natalia A. Viana Bedoya
Universidade Federal de São Carlos
https://www.researchgate.net/scientific-contributions/Natalia-A-Viana-Bedoya-84997682
Date(s) : 11/09/2017 iCal
14h00 - 15h00
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.
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