The index of Floer moduli problems for parametrized action functionals

TL;DR

This paper introduces an index for critical points of parametrized Hamiltonian action functionals, linking it to the expected dimension of moduli spaces of Floer trajectories, advancing the understanding of parametrized Floer theory.

Contribution

It defines a new index for parametrized Hamiltonian action functionals and relates it to the dimension of moduli spaces, providing a foundational tool for parametrized Floer theory.

Findings

Defined an index for critical points of parametrized Hamiltonian action functionals.

Established that the expected dimension of moduli spaces equals the difference of indices of asymptotes.

Provided a framework for analyzing parametrized Floer trajectories.

Abstract

We define an index for the critical points of parametrized Hamiltonian action functionals. The expected dimension of moduli spaces of parametrized Floer trajectories equals the difference of indices of the asymptotes.