Generating families on arboreal graphs

TL;DR

This paper introduces the concept of generating families for exact curves on Arborealized Liouville surfaces and proves a Hamiltonian lifting property, contributing to symplectic geometry and future research directions.

Contribution

It defines generating families for curves on Arborealized Liouville surfaces and establishes their Hamiltonian invariance, advancing the understanding of symplectic invariants.

Findings

Set of curves with generating families is Hamiltonian isotopy invariant

Established a Hamiltonian lifting property for these curves

Lays groundwork for future generalizations and applications

Abstract

The paper is devoted to the study of exact curves on Arborealized Liouville surfaces. We introduce the notion of a generating family for such curves. Our main statement is a hamiltonian lifting property: the set of curves admitting a generating family is closed with respect to Hamiltonian isotopes. This is part of the author's future thesis. It will be translated into English within a few weeks. In the future, we plan to generalize our results in several directions and find applications.