A homotopical viewpoint at the Poisson bracket invariants for tuples of sets

TL;DR

This paper introduces a homotopical approach to understanding Poisson bracket invariants for tuples of closed sets in symplectic manifolds, revealing their dependence on topological data and set unions.

Contribution

It provides a novel homotopical framework for Poisson bracket invariants, emphasizing their topological nature and dependence on set unions.

Findings

Poisson bracket invariants depend only on the union of sets and topological data

Homotopical description simplifies understanding of invariants

Invariance under topological transformations

Abstract

We suggest a homotopical description of the Poisson bracket invariants for tuples of closed sets in symplectic manifolds. It implies that these invariants depend only on the union of the sets along with topological data.