Homotopy derivations of the framed little discs operads

TL;DR

This paper investigates the homotopy derivations of framed little discs operads, linking them to the cohomology of graph complexes and extending previous results to BV2n operads.

Contribution

It provides a new description of homotopy derivations of BV2n operads via graph complex cohomology, extending Willwacher's work on en operads.

Findings

Homotopy derivations of BV2n operads are described through graph complex cohomology.

An explicit quasi-isomorphic map is constructed.

The work extends known results from en operads to BV2n operads.

Abstract

We study the homotopy derivations of the framed little discs operads, which correspond to the homotopy derivations of the BV2n operads. By extending a result by Willwacher about the homotopy derivations of the en operads we show that the homotopy derivations of the BV2n operads may be described through the cohomology of a suitable graph complex. We will present an explicit quasi-isomorphic map.