Matroids, Feynman categories, and Koszul duality
Combinatorics
2024-12-12 v3 Algebraic Topology
Category Theory
Abstract
We show that various combinatorial invariants of matroids such as Chow rings and Orlik--Solomon algebras may be assembled into "operad-like" structures. Specifically, one obtains several operads over a certain Feynman category which we introduce and study in detail. In addition, we establish a Koszul-type duality between Chow rings and Orlik--Solomon algebras, vastly generalizing a celebrated result of Getzler. This provides a new interpretation of combinatorial Leray models of Orlik--Solomon algebras.
Cite
@article{arxiv.2211.12370,
title = {Matroids, Feynman categories, and Koszul duality},
author = {Basile Coron},
journal= {arXiv preprint arXiv:2211.12370},
year = {2024}
}
Comments
Final version. To appear in The Duke Mathematical Journal