Arborealization of Lagrangian skeleta
Motivated by microlocal sheaf theory, Nadler introduced a particularly simple and natural class of singularities for the Lagrangian skeleta of Weinstein manifolds. These singularities are called arboreal, and skeleta with only arboreal singularities are called arboreal skeleta. Unlike generic Lagrangian skeleta, arboreal skeleta have unique Weinstein neighborhoods and offer the hope of reducing pseudo-holomorphic curve invariants of Weinstein manifolds to combinatorics. In work in progress joint with Eliashberg, Nadler and Starkston we study the problem of existence and uniqueness of arboreal skeleta for Weinstein manifolds, which is intimately linked to the problem of simplifying the singularities of Lagrangian and Legendrian fronts. In this talk we will discuss our current understanding of the problem.