Multi-directed graph complexes and quasi-isomorphisms between them I: oriented graphs
Quantum Algebra
2018-02-14 v2
Abstract
We construct a direct quasi-isomorphism from Kontsevich's graph complex GC_n to the oriented graph complex 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 GC_n and 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.
Keywords
Cite
@article{arxiv.1703.09605,
title = {Multi-directed graph complexes and quasi-isomorphisms between them I: oriented graphs},
author = {Marko Živković},
journal= {arXiv preprint arXiv:1703.09605},
year = {2018}
}