Reference : Multi-directed Graph Complexes and Quasi-isomorphisms Between Them II: Sourced Graphs
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/40977
Multi-directed Graph Complexes and Quasi-isomorphisms Between Them II: Sourced Graphs
English
Zivkovic, Marko mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
4-Nov-2019
International Mathematics Research Notices
Oxford University Press
00
0
1-57
Yes (verified by ORBilu)
International
1073-7928
1687-0247
Oxford
United Kingdom
[en] Graph complexes
[en] We prove that the projection from graph complex with at least one source to oriented graph complex is a quasi-isomorphism, showing that homology of the “sourced” graph complex is also equal to the homology of standard Kontsevich’s graph complex. This result may have applications in theory of multi-vector fields T≥1poly of degree at least one, and to the hairy graph complex that computes the rational homotopy of the space of long knots. The result is generalized to multi-directed graph complexes, showing that all such graph complexes are quasi-isomorphic. These complexes play a key role in the deformation theory of multi-oriented props recently invented by Sergei Merkulov. We also develop a theory of graph complexes with arbitrary edge types.
Researchers ; Professionals
http://hdl.handle.net/10993/40977
10.1093/imrn/rnz212
https://doi.org/10.1093/imrn/rnz212

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