Classes D'homotopie de Surfaces Avec Rebroussements et Queues D'aronde dans ℝ3

Abstract

RésuméWe consider surfaces in ℝ3 with generic wave front singularities, called A-mersions (A for Arnold who classified these singularities), we classify A-mersions up to generic homotopy. For the sphere they are classified by the degree of the Gauss map, and for higher genus surfaces the degree of the Gauss map and the number of zig-zags classify the A-mersion.