Cohomology of a Quaternionic Complex

TL;DR

This paper studies the cohomology of a specific elliptic complex on compact quaternionic-Kähler manifolds with negative scalar curvature, revealing its near-exactness with only one potential exception.

Contribution

It demonstrates the exactness of a particular elliptic complex on these manifolds, advancing understanding of their cohomological properties.

Findings

The elliptic complex is exact on compact quaternionic-Kähler manifolds with negative scalar curvature.

Potential exception identified at one term in the complex.

Provides new insights into the cohomological structure of quaternionic-Kähler manifolds.

Abstract

We investigate the cohomology of a certain elliptic complex defined on a compact quaternionic-K\"{a}hler manifold with negative scalar curvature. We show that this particular complex is exact, with the possible exception of one term.