The Calabi invariant for some groups of homeomorphisms

TL;DR

This paper extends the Calabi homomorphism to certain groups of homeomorphisms on exact symplectic manifolds, leveraging the uniqueness of generating Hamiltonians for continuous Hamiltonian isotopies.

Contribution

It introduces a method to extend the Calabi homomorphism to broader groups of homeomorphisms using recent results on Hamiltonian isotopies.

Findings

Calabi homomorphism successfully extended to some homeomorphism groups

Utilizes the uniqueness of generating Hamiltonians for continuous isotopies

Provides a new framework for symplectic topology analysis

Abstract

We show that the Calabi homomorphism extends to some groups of homeomorphisms on exact symplectic manifolds. The construction is based on the uniqueness of the generating Hamiltonian (proved by Viterbo) of continuous Hamiltonian isotopies (introduced by Mueller and Oh).