Poisson structures in the Banach setting: comparison of different approaches

TL;DR

This paper compares different approaches to defining Poisson manifolds within Banach manifolds, highlighting their differences through examples and analyzing their implications.

Contribution

It systematically examines and contrasts various existing definitions of Poisson structures in the Banach setting, clarifying their relationships.

Findings

Different definitions of Poisson manifolds in Banach spaces are compared.

Illustrative examples highlight the distinctions between approaches.

The paper clarifies the implications of each approach for the theory.

Abstract

In this paper we examine various approaches to the notion of Poisson manifold in the context of Banach manifolds. Existing definitions are presented and differences between them are explored and illustrated with examples.