Vortrag im Schwerpunkt Reelle Geometrie und Algebra
Freitag, 18. Dezember 2009, um 14:15 Uhr in F426 (Oberseminar) Olivier Le Gal (Chambéry) A generic condition implying o-minimality for restricted smooth functions
Let h:[0,1]->R be a restricted smooth function. The structure Rh generated by h is the collection of all the objects that can be geometrically obtained from h and polynomial maps. The structure Rh is o-minimal when the sets in Rh have a "tame" topology. This o-minimality implies in particular that all the germs of h live in a hardy field which is stable under composition. When this hardy fields has rank 1, the structure is said to be polynomially bounded.
We will present a condition on h which implies that Rh is o-minimal and polynomially bounded. We also prove that this condition is generic for the Whitney topology. As corollaries, we obtain o-minimal structures that do not admit analytic cell decomposition, and non compatible o-minimal structures.
