Lagrangian cobordism and metric invariants

TL;DR

This paper introduces new pseudo-metrics on Lagrangian submanifold spaces using projections of cobordisms, exploring their non-degeneracy and implications for symplectic rigidity and flexibility.

Contribution

It presents novel pseudo-metrics based on Lagrangian cobordisms and analyzes their non-degeneracy, advancing understanding of symplectic topology.

Findings

Pseudo-metrics reflect rigidity and flexibility of Lagrangian cobordisms

Non-degeneracy properties are established for the introduced pseudo-metrics

Insights into symplectic invariants and Lagrangian topology

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.