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UID:7503@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170911T140000
DTEND;TZID=Europe/Paris:20170911T150000
DTSTAMP:20241120T204349Z
URL:https://www.i2m.univ-amu.fr/evenements/branched-covering-over-the-sphe
 re/
SUMMARY:Natalia A. Viana Bedoya (Universidade Federal de São Carlos): Bran
 ched covering over the sphere
DESCRIPTION:Natalia A. Viana Bedoya: A branched covering of degree d over t
 he 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. Ed
 monds\, R. Kulkarni and R. Stong exhibit\, for any non-prime integer d\, a
 n exceptional collection\, i.e. a collection of partitions satisfying the 
 necessary conditions but that is not realizable as a branch datum of any b
 ranched covering over S^2.\n\nThis realization problem is still open. It w
 as completely solved just for collections involving a "short" partition li
 ke :\n1. [d]\, by R. Thom in 1965\, via complex polynomials\;\n2. [d-1\,1]
 \, by A. Edmonds\, R. Kulkarni and R. Stong in 1984\, via permutation grou
 ps\;\n3. [d-2\,2]\, by E. Pervova and C. Petronio in 2008\, via minimal ch
 ecker-board graphs.\nFor other collections are known\, at most\, partial r
 esults.\n\nIn this talk\, I would like to introduce the problem and some o
 f the techniques used to study it.\n&nbsp\;
CATEGORIES:Séminaire,Dynamique et Topologie
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