A stable homotopy invariant for Legendrians with generating families
Abstract
We construct a stable homotopy type invariant for any Legendrian submanifold in a jet bundle equipped with a linear-at-infinity generating family. We show that this spectrum lifts the generating family homology groups. When the generating family extends to a generating family for an embedded Lagrangian filling, we lift the Seidel isomorphism to the spectrum level. As applications, we establish topological constraints on Lagrangian fillings arising from generating families, algebraic constraints on whether generating families admit fillings, and lower bounds on how many fiber dimensions are needed to construct a generating family for a Legendrian.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Topological and Geometric Data Analysis
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Journal of Symplectic Geometry
- Volume
- 24
- Issue
- 2
- Pages
- 371–466
- Publication date
- 1 January 2026
- Language
- EN