We show that the knot type of the link of a real analytic map germ with isolated singularity is a complete invariant for --equivalence. Moreover, we also prove that isolated singularity implies finite -determinacy, giving an explicit estimate for its degree. For the general case of real analytic map germs, (), we use the Lojasiewicz exponent associated with Mond’s double point ideal to obtain some criteria of Lipschitz and analytic regularity.
"Topological Classification and Finite Determinacy of Knotted Maps." Michigan Math. J. 69 (4) 831 - 848, October 2020. https://doi.org/10.1307/mmj/1585792886