Higher Structures, Vol. 4, No. 1, pp. 266-283, 2020
Multi-directed graph complexes and quasi-isomorphisms between them I: oriented graphs
Marko Živković
Received February 13th 2018. Published online February 11th 2020.
Abstract: We construct a direct quasi-isomorphism from Kontsevich’s graph complex ${\bf GC}_n$ to the oriented graph complex ${\bf OGC}_{n+1}$, 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 ${\bf GC}_n$ and ${\bf OGC}_{n+1}$ are the first two members. These complexes play a key role in the deformation theory of multi-oriented props recently invented by Sergei Merkulov.
