Geodesic
Cacti, Braids and Complex Polynomials
Séminaire lotharingien de combinatoire, Tome 37 (1996)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

The study of the topological classification of complex polynomials began in the XIX-th century by Luroth, Clebsch and Hurwitz. In the works of Zdravkovska and Khovanskii the problem is reduced to a purely combinatorial one, namely the study of a certain action of the braid groups on a class of tree-like figures that we, following Goulden and Jackson, call "cacti".

Using explicit computation of the braid group orbits, enumerative results of Goulden and Jackson, and also establishing some combinatorial invariants of the action, we provide the topological classification of polynomials of degree up to 9 (previous results were known up to degree 6). 

@article{SLC_1996_37_a1,
     author = {Mohamed El Marraki and Nicolas Hanusse and J\"org Zipperer and Alexander Zvonkin},
     title = {Cacti, {Braids} and {Complex} {Polynomials}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {37},
     year = {1996},
     url = {http://geodesic.mathdoc.fr/item/SLC_1996_37_a1/}
}
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AU  - Nicolas Hanusse
AU  - Jörg Zipperer
AU  - Alexander Zvonkin
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JO  - Séminaire lotharingien de combinatoire
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%A Jörg Zipperer
%A Alexander Zvonkin
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%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_1996_37_a1/
%F SLC_1996_37_a1
Mohamed El Marraki; Nicolas Hanusse; Jörg Zipperer; Alexander Zvonkin. Cacti, Braids and Complex Polynomials. Séminaire lotharingien de combinatoire, Tome 37 (1996). http://geodesic.mathdoc.fr/item/SLC_1996_37_a1/