A’Campo’s forests for the space of complex polynomials

Prelegent(ci)

Noemie Combe

Afiliacja

Institut de Mathématiques de Marseille

Termin

2 czerwca 2017 10:15

Pokój

p. 5840

Seminarium

Seminarium Zakładu Układów Dynamicznych

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A new cellulation for the space of complex, polynomials 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 $S^{2}$. Using Łojasiewicz'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.
 

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