# Bigraded cochain complexes and Poisson cohomology

## TL;DR

This paper develops an algebraic framework for computing low-degree cohomology in bigraded complexes related to Poisson geometry and Lie algebroids, enabling concrete calculations in specific cases.

## Contribution

It introduces a novel algebraic method for low-degree cohomology computation applicable to Poisson structures and Lie algebroids.

## Key findings

- Framework simplifies cohomology calculations
- Applicable to Poisson geometry around (pre)symplectic leaves
- Successfully computes cohomology in example cases

## Abstract

We present an algebraic framework for the computation of low-degree cohomology of a class of bigraded complexes which arise in Poisson geometry around (pre)symplectic leaves. We also show that this framework can be applied to the more general context of Lie algebroids. Finally, we apply our results to compute the low-degree cohomology in some particular cases.