Action selectors and Maslov class rigidity

TL;DR

This paper introduces new restrictions on the Maslov class of displaceable Lagrangian submanifolds in symplectically aspherical manifolds, using novel action selectors related to Hamiltonian flow minimization.

Contribution

It develops a new action selector for specific Hamiltonian flows, providing novel restrictions on the Maslov class of certain Lagrangian submanifolds.

Findings

Established new Maslov class restrictions for displaceable Lagrangians

Constructed a novel action selector for Hamiltonian flows

Applied the selector to Hamiltonian paths minimizing Hofer length

Abstract

In this paper we detect new restrictions on the Maslov class of displaceable Lagrangian submanifolds of symplectic manifolds which are symplectically aspherical. These restrictions are established using action selectors for Hamiltonian flows. In particular, we construct and utilize a new action selector for the flows of a special class of Hamiltonian functions which arises naturally in the study of Hamiltonian paths which minimize the Hofer length functional.