Multi-directed graph complexes and quasi-isomorphisms between them I: oriented graphs

Marko Zivkovic

Abstract


We construct a direct quasi-isomorphism from Kontsevich's graph complex GCn to the oriented graph complex OGCn+1, thus providing an alternative proof that the two complexes are quasi-isomorphic. Moreover, the result is extended to the sequence of multi-oriented graph complexes, where GCn and OGCn+1 are the first two members. These complexes play a key role in the deformation theory of multi-oriented props recently invented by Sergei Merkulov.

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