Geomorphology of Lagrangian ridges

We prove an ‘h-principle without pre-conditions’ for the elimination of tangencies of a Lagrangian submanifold with respect to a Lagrangian distribution. The main result states that such tangencies can always be completely removed at the cost of allowing the Lagrangian to develop certain non-smooth points, called Lagrangian ridges, modeled on the corner { p = | q | } ⊂ R 2 $\lbrace p=|q|\rbrace \subset \mathbb {R}^2$ together with its products and stabilizations. This result plays an essential role in the arborealization program.