Invariants of Lagrangian cobordisms via spectral numbers

TL;DR

This paper extends spectral invariants to Lagrangian cobordisms, introducing a spectral metric and new invariants that help quantify and compute Lagrangian cobordism properties.

Contribution

It develops a spectral invariant framework for Lagrangian cobordisms, providing new metrics, invariants, and computational methods.

Findings

Introduces a nondegenerate spectral metric bounding the cobordism metric.

Provides a new numerical Lagrangian cobordism invariant.

Enables explicit computation of asymptotic spectral invariants.

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.