Topological Classification and Finite Determinacy of Knotted Maps

Abstract

We show that the knot type of the link of a real analytic map germ with isolated singularity f : ( R 2 , 0 ) → ( R 4 , 0 ) is a complete invariant for C 0 - A -equivalence. Moreover, we also prove that isolated singularity implies finite C 0 -determinacy, giving an explicit estimate for its degree. For the general case of real analytic map germs, f : ( R n , 0 ) → ( R p , 0 ) ( n ≤ p ), we use the Lojasiewicz exponent associated with Mond’s double point ideal I 2 ( f ) to obtain some criteria of Lipschitz and analytic regularity.