[en] 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.
Disciplines :
Mathematics
Author, co-author :
Zivkovic, Marko ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
'Multi-directed graph complexes and quasi-isomorphisms between them I: oriented graphs
Publication date :
2020
Journal title :
Higher Structures
ISSN :
2209-0606
Publisher :
Macquarie Univ., Dept. Math., North Ryde, New South Wales, Australia
