A hypergraph model for the cyclic BV operad and its applications

Sergei Merkulov

paper

A hypergraph model for the cyclic BV operad and its applications

arXiv:2603.23368

Abstract

A dg cyclic operad $B V H g r a p h s$ of hypergraphs is introduced which comes equipped with an explicit quasi-isomorphism $B V \to B V H g r a p h s$ from the { cyclic} operad $B V$ of Batalin-Vilkovisky algebras. A proof that the cohomology of $B V H g r a p h s$ equals $B V$ occupies most of this paper. We use this model to construct an explicit quasi-isomorphism $C hain s (F F M_{2}) \to B V H g r a p h s$ from the chain operad of the cyclic operad $F F M_{2}$ of the compactified moduli spaces of genus zero curves with marked framed points to the dg cyclic operad $B V H g r a p h s$ which, combined with the main result mentioned above, gives a new proof of the cyclic formality of $F F M_{2}$ .