Let f: (R2, 0) → (R2, 0) be a finitely determined map germ. The link of f is obtained by taking a small enough representative f: U ⊂ R2 → R2 and the intersection of its image with a small enough sphere Sε1 centered at the origin in R2. We will describe the topology of f in terms of the Gauss word associated to its link.
"The link of a finitely determined map germ from R2 to R2." J. Math. Soc. Japan 62 (4) 1069 - 1092, October, 2010. https://doi.org/10.2969/jmsj/06241069