| Title:
|
Multi-directed graph complexes and quasi-isomorphisms between them I: oriented graphs (English) |
| Author:
|
Živković, Marko |
| Language:
|
English |
| Journal:
|
Higher Structures |
| ISSN:
|
2209-0606 |
| Volume:
|
4 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
266-283 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
Graph Complexes |
| Keyword:
|
Multi-directed graph complexes |
| Keyword:
|
Multi-oriented props |
| Keyword:
|
Oriented graph complexes |
| MSC:
|
16E45 |
| MSC:
|
18G55 |
| MSC:
|
53C15 |
| MSC:
|
53D55 |
| idZBL:
|
Zbl 1434.05156 |
| idMR:
|
MR4074277 |
| DOI:
|
10.21136/HS.2020.06 |
| . |
| Date available:
|
2026-03-11T21:44:44Z |
| Last updated:
|
2026-03-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153421 |
| . |
| Reference:
|
[1] Khoroshkin, Anton, Willwacher, Thomas, Živković, Marko: Differentials on graph complexes..Adv. Math. 307:1184–1214 |
| Reference:
|
[2] Kontsevich, Maxim: Formal (non)commutative symplectic geometry..In Proceedings of the I. M. Gelfand seminar 1990–1992, 173–-188. Birkhauser |
| Reference:
|
[3] Kontsevich, Maxim: Formality Conjecture..Deformation Theory and Symplectic Geometry 139–156. D. Sternheimer et al. (eds.) |
| Reference:
|
[4] Merkulov, Sergei: Multi-oriented props and homotopy algebras with branes..arxiv:1712.09268 http://arxiv.org/pdf/1712.09268 |
| Reference:
|
[5] Merkulov, Sergei: Deformation quantization of homotopy algebras with branes..arxiv:1712.09268 http://arxiv.org/pdf/1712.09268 |
| Reference:
|
[6] Merkulov, S., Vallette, B.: Deformation theory of representations of prop(erad)s I & II..Journal für die reine und angewandte Mathematik. (Qrelle) 634: 51–106 & 636: 123–174 |
| Reference:
|
[7] Merkulov, Sergei, Willwacher, Thomas: Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves..arxiv:1511.07808 http://arxiv.org/pdf/1511.07808 |
| Reference:
|
[8] Willwacher, Thomas: M. Kontsevich’s graph complex and the Grothendieck-Teichmüller Lie algebra..Invent. Math. 200(3):671–760 |
| Reference:
|
[9] Willwacher, Thomas: The oriented graph complexes..Commun. Math. Phys. 334: 1649 10.1007/s00220-014-2168-9 |
| Reference:
|
[10] Willwacher, Thomas, Živković, Marko: Multiple edges in M. Kontsevich’s graph complexes and computations of the dimensions and Euler characteristics..Adv. Math. 272:553–578 |
| Reference:
|
[11] Živković, Marko: Multi-directed graph complexes and quasi-isomorphisms between them II: Sourced graphs..Int. Math. Res. Notices, rnz212, https://doi.org/10.1093/imrn/rnz212 10.1093/imrn/rnz212 |
| . |
