English

Poincar\'e/Koszul Duality for General Operads

Algebraic Topology 2021-08-03 v3

Abstract

We record a result concerning the Koszul dual of the arity filtration on an operad. This result is then used to give conditions under which, for a general operad, the Poincar\'e/Koszul duality arrow of Ayala-Francis is an equivalence. We discuss how the Poincar\'e/Koszul duality arrow for the little nn-disks operad En\mathcal{E}_n relates to their work when combined with the self-Koszul duality of En\mathcal{E}_n.

Cite

@article{arxiv.1910.09076,
  title  = {Poincar\'e/Koszul Duality for General Operads},
  author = {Araminta Amabel},
  journal= {arXiv preprint arXiv:1910.09076},
  year   = {2021}
}

Comments

Revised after referee comments

R2 v1 2026-06-23T11:49:13.975Z