Finiteness theorem for topological contact equivalence of map germs

Abstract

Let $P^{k}(n,2)$ be the set of all real polynomial map germs $f=(f_1,f_2):(\mathbb R^n,0) \rightarrow (\mathbb R^2,0)$ with degree of $f_1,f_2 \leq k$. 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.