A note on partial quasi-morphisms and products in Lagrangian Floer homology in cotangent bundles

TL;DR

This paper introduces partial quasi-morphisms on Hamiltonian diffeomorphisms of cotangent bundles using spectral invariants from Lagrangian Floer homology, addressing the lack of a compatible product structure.

Contribution

It defines partial quasi-morphisms in cotangent bundles via spectral invariants, extending Floer homology tools without relying on a compatible product.

Findings

Constructed partial quasi-morphisms using spectral invariants.

Established properties of these quasi-morphisms in cotangent bundles.

Addressed the absence of a compatible product in the Floer homology setting.

Abstract

We define partial quasi-morphisms on the group of Hamiltonian diffeomorphisms of the cotangent bundle using the spectral invariants in Lagrangian Floer homology with conormal boundary conditions, where the product compatible with the PSS isomorphism and the homological intersection product is lacking.