A proof of the Hamiltonian Thom Isotopy Lemma

TL;DR

This paper provides a complete proof that all submanifolds in a one-parameter family of compact symplectic submanifolds within a compact symplectic manifold are Hamiltonian isotopic, confirming a key theoretical result.

Contribution

It offers the first complete proof of the Hamiltonian Thom Isotopy Lemma for compact symplectic submanifolds.

Findings

All submanifolds in the family are Hamiltonian isotopic.

The proof solidifies the theoretical foundation of symplectic topology.

Supports further research in symplectic isotopy classes.

Abstract

In this note we present a complete proof of the fact that all the submanifolds of a one parameter family of compact symplectic submanifolds inside a compact symplectic manifold are Hamiltonian isotopic.