ABSTRACT

In this section, we review Viro’s reconstruction of Arnold invariant J−. Let C be an oriented plane curve that is the image of a generic immersion from an oriented circle into a plane. Because the curve C is the image of a generic immersion, C = fC(S

1), where for each t ∈ S1, fC(t) = x ∈ C ⊂ R2. Now we select and fix a point a ∈ R2 \ C. Then, we consider the map C → S1 such that

ga : x 7→ x− a

|x− a| .