On non-geometric augmentations in high dimensions

In this note we construct augmentations of Chekanov-Eliashberg algebras of certain high dimensional Legendrian submanifolds that are not induced by exact Lagrangian fillings. The obstructions to the existence of exact Lagrangian fillings that we use are Seidel’s isomorphism and the injectivity of a certain algebraic map between the corresponding augmentation varieties proven by Gao and Rutherford. In addition, along the way we discuss the relation between augmentation varieties of Legendrian submanifolds and their spherical spuns.