Proof of Arnold's 4 cusp conjecture
(joint work with P. Pushkar)
(joint work with P. Pushkar)
The conjecture deals with fronts in the plane. Fronts are curves that generically can have as singularities transverse crossings and semi-cubic cusps. Such curves naturally arise as wavefronts. The Arnold's 4 cusp conjecture claims that in every generic path in the space of co-oriented fronts without oriented self-tangencies that connects two embedded circles with opposite co-orientations there exists a front with at least 4 cusps.