This work establishes an equivalence relation for Lagrangians and reveals the non-torsion nature of the Lagrangian Ceresa cycle, suggesting implications for tropical flux.
Key Points
The Lagrangian Ceresa cycle is proven to be non-torsion in its algebraic Lagrangian cobordism group, supporting deep interactions between symplectic geometry and algebraic cycles.
Tropical curves are shown to have a corresponding Lagrangian lift that remains non-torsion, indicating the richness of the relationship between different geometric objects.
Developments include the introduction of tropical and symplectic flux, establishing morphisms that connect Griffiths and Lagrangian cobordism groups.
This research signals significant advancements in understanding the algebraic equivalences and the role of cycles in higher-dimensional geometries.