On the Lagrangian Hofer geometry in symplectically aspherical manifolds

TL;DR

This paper demonstrates the embedding of normed linear spaces into the Hamiltonian deformation space of Lagrangian submanifolds in symplectically aspherical manifolds using spectral invariants, expanding understanding of Lagrangian Hofer geometry.

Contribution

It introduces a method to embed linear spaces into Lagrangian Hofer metric spaces via spectral invariants, providing new explicit examples and generalizing existing results.

Findings

Explicit isometric embeddings into Lagrangian Hofer spaces.

New examples where the Hofer metric can be computed explicitly.

Refined and generalized previous results on Lagrangian Hofer geometry.

Abstract

We use spectral invariants in Lagrangian Floer theory in order to show that there exist \emph{isometric} embeddings of normed linear spaces (finite or infinite dimensional, depending on the case) into the space of Hamiltonian deformations of certain Lagrangian submanifolds in tame symplectically aspherical manifolds. In addition to providing a new class of examples in which the Lagrangian Hofer metric can be computed explicitly, we refine and generalize some known results about it.