Hokkaido Mathematical Journal

BIRBRAIR Lev, COSTA Jo\~{a}o Carlos Ferreira, FERNANDES Alexandre,

Finiteness theorem for topological contact equivalence of map germs.

Hokkaido Mathematical Journal, 38 (2009) pp.511-517

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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.

MSC(Primary)32S15
MSC(Secondary)32S05
Uncontrolled Keywordstopological contact equivalence, finiteness theorem.