The link of a finitely determined map germ from R2 to R2

Some remarks about the topology of corank 2 map germs from R^2 to R^2

“…The fact that we are not able to consider our germs as 1-parameter unfoldings of functions, as we did in the corank 1 case, makes things to become much more complex. The absolute value of the topological degree does not have to be necessarily less or equal than 1 and although our Gauss words continue being a complete topological invariant, since their links are not constituted as the union of 2 curves (as we did in [9]) the simplifications of letters are not allowed anymore.…”

“…In this section we recall briefly (for more information and examples see [9]) how we define an adapted version of the Gauss word in our particular case of study and some consequences of such definition. Definition 3.1.…”

“…In a previous paper [9] we defined the Gauss word, which is a complete topological invariant for a finitely determined map germ f : (R 2 , 0) → (R 2 , 0) and we used it to classify corank 1 map germs. The following logical step is to try to extend this classification to germs of corank 2.…”

On polynomial mappings from the plane to the plane

“…In particular, there are results concerning p µ(p), where p runs through the set of cusp points (see [3], [11]). Singularities of map germs of the plane into the plane were studied in [3], [4], [8], [10]. For a recent account of the subject, and other related results, we refer the reader to [2], [12].…”

“…(8) and Theorem 1, the signature of Θ 2 equals p∈Σ sgn DF (p) = p∈Σ µ(p). Assertion (iii) is now obvious.…”