Canonical forms of oriented matroids
Abstract
Abstract Positive geometries are semialgebraic sets equipped with a canonical differential form whose residues mirror the boundary structure of the geometry. Every full‐dimensional projective polytope is a positive geometry. Motivated by the canonical forms of polytopes, we construct a canonical form for any tope of an oriented matroid inside the Orlik–Solomon algebra of the underlying matroid. Using these canonical forms, we construct bases for the Orlik–Solomon algebra of a matroid and for the Aomoto cohomology. These bases of canonical forms are a foundational input in the theory of matroid amplitudes introduced by the second author.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Homotopy and Cohomology in Algebraic Topology
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 1
- Publication date
- 1 January 2026
- Language
- EN