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Keywords:
Graph Complexes; Multi-directed graph complexes; Multi-oriented props; Oriented graph complexes
Graph Complexes; Multi-directed graph complexes; Multi-oriented props; Oriented graph complexes
Summary:
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.
References:
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