Abstract
We introduce new pseudo-metrics on spaces of Lagrangian submanifolds of a symplectic manifold $(M, \omega)$ by considering areas associated to projecting Lagrangian cobordisms in $\mathbb{C} \times M$ to the “time-energy plane” $\mathbb{C}$. We investigate the non-degeneracy properties of these pseudo-metrics, reflecting the rigidity and flexibility aspects of Lagrangian cobordisms.
Funding Statement
The first author was supported by an NSERC Discovery grant, a FQRNT Group Research grant, a Simons Fellowship and an Institute for Advanced Study fellowship grant. The second author was partially supported by the National Science Foundation under agreement No. DMS-1128155.
Citation
Octav Cornea. Egor Shelukhin. "Lagrangian cobordism and metric invariants." J. Differential Geom. 112 (1) 1 - 45, May 2019. https://doi.org/10.4310/jdg/1557281005
