Arboreal models and their stability (Q6055556)

Arboreal singularities were introduced by \textit{D. Nadler} [Geom. Topol. 21, No. 2, 1231--1274 (2017; Zbl 1420.57071)]. This paper is part of a series of papers written by the authors on the classification and geometry of arboreal singularities. The main result is a uniqueness theorem stating that the ambient symplectomorphism classes of signed arboreal Lagrangian and Legendrian singularities are determined by their combinatorial type. Moreover, it is shown that each combinatorial type has a canonical local model described by polynomial equations.