On non-geometric augmentations in high dimensions

Abstract

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.

arXiv comment10 pages, 2 figures, final version

References in corpus (9)

• Lagrangian concordance of Legendrian knots
• An atlas of Legendrian knots
• Lifting pseudo-holomorphic polygons to the symplectisation of $P\times \mathbb{R}$ and applications
• A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}
• A note on the front spinning construction
• A note on infinite number of exact Lagrangian fillings for spherical spuns
• Estimating the number of Reeb chords using a linear representation of the characteristic algebra
• Nonfillable Legendrian knots in the 3-sphere
• On Legendrian products and twist spuns