|Responsables :||Catherine Gille et Najib Idrissi|
|Email des responsables :|
|Adresse :||Sophie Germain|
|Orateur(s)||Noémie Combe - Université d'Aix-Marseille,|
|Titre||A’Campo’s forests for the space of complex polynomials|
|Horaire||11:00 à 12:00|
|Résume||A new cellulation for the space of complex polynomials P is given. Each polynomial is characterized by A’Campo's ``geometric pictures’’ which are bi-colored planar graphs. These A’Campo forests provide a semi-algebraic stratification for the space. The strata are contractible by Riemann's theorem on the conformal structure of S².
Using Lojasiewicz's triangulation, we provide a new cell decomposition. From this cell decomposition follows the cohomology groups for the space of polynomials.
This approach is reminiscent of the Grothendieck ``dessin d'enfants'', but is far from the construction of Grothendieck, Penner and Shabat-Voevodsky, concerning only polynomials having two critical values.