# A cohomological characterization of nilpotent fusion systems

## TL;DR

This paper introduces a cohomological criterion to determine when a fusion system is nilpotent, linking algebraic properties with topological invariants.

## Contribution

It offers a novel nilpotency criterion for fusion systems based on the vanishing of their cohomology with twisted coefficients.

## Key findings

- Cohomology with twisted coefficients characterizes nilpotent fusion systems.
- Provides a practical criterion for identifying nilpotency.
- Connects algebraic and topological aspects of fusion systems.

## Abstract

We provide a nilpotency criterion for fusion systems in terms of the vanishing of its cohomology with twisted coefficients.