Invariants of Lagrangian cobordisms via spectral numbers

Abstract

We extend parts of the Lagrangian spectral invariants package recently developed by Leclercq and Zapolsky to the theory of Lagrangian cobordism developed by Biran and Cornea. This yields a nondegenerate Lagrangian "spectral metric" which bounds the Lagrangian "cobordism metric" (recently introduced by Cornea and Shelukhin) from below. It also yields a new numerical Lagrangian cobordism invariant as well as new ways of computing certain asymptotic Lagrangian spectral invariants explicitly.

25 pages, 1 figure, v3: Major revision. Added new results on non-degeneracy of spectral metric. Final version. To appear in Journal of Topology and Analysis