Abstract
We recall the construction of the Kontsevich graph orientation morphism which maps cocycles γ in the non-oriented graph complex to infinitesimal symmetries of Poisson bi-vectors on affine manifolds. We reveal in particular why there always exists a factorization of the Poisson cocycle condition through the differential consequences of the Jacobi identity for Poisson bi-vectors . To illustrate the reasoning, we use the Kontsevich tetrahedral flow , as well as the flow produced from the Kontsevich–Willwacher pentagon-wheel cocycle γ5 and the new flow obtained from the heptagon-wheel cocycle γ7 in the unoriented graph complex.
Highlights
On an affine manifold M r, the Poisson bi-vector fields are those satisfying the Jacobi identity [[P, P]] = 0, where [[·, ·]] is the Schouten bracket [12, see Example 1 below]
We reveal in particular why there factorization of the Poisson cocycle condition [[P, O⃗r(γ)(P)]] =. 0 through the differential consequences of the Jacobi identity [[P, P]] = 0 for Poisson bi-vectors P
We use the Kontsevich tetrahedral flow P = O⃗r(γ3)(P), as well as the flow produced from the Kontsevich–Willwacher pentagon-wheel cocycle γ5 and the new flow obtained from the heptagon-wheel cocycle γ7 in the unoriented graph complex
Summary
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Document Version Publisher's PDF, known as Version of record. Citation for published version (APA): Buring, R., & Kiselev, A. More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverneamendment. Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. To cite this article: Ricardo Buring and Arthemy V Kiselev 2019 J.
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