English

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}
}
R2 v1 2026-06-22T18:59:27.766Z