Finiteness theorem for topological contact equivalence of map germs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Processo FAPESP: 07/01274-6

Let p(k) (n, 2) be the set of all real polynornial map germs f = (f(1), f(2)) : (R(n), 0) -> (R(2), 0) with degree of f(1), f(2) <= k. The main result of this paper shows that the set of equivalence classes of p(k) (n, 2), with respect to topological contact equivalence, is finite.