Differentials on graph complexes

Anton Khoroshkin, Thomas Willwacher, Marko Živković

Research output: Contribution to journalArticlepeer-review


We study the cohomology of complexes of ordinary (non-decorated) graphs, introduced by M. Kontsevich. We construct spectral sequences converging to zero whose first page contains the graph cohomology. In particular, these spectral sequences may be used to show the existence of an infinite series of previously unknown and provably non-trivial cohomology classes, and put constraints on the structure of the graph cohomology as a whole.

Original languageEnglish
Pages (from-to)1184-1214
Number of pages31
JournalAdvances in Mathematics
StatePublished - 5 Feb 2017
Externally publishedYes

Bibliographical note

Funding Information:
A.Kh. research has been supported by the RFBR grant 15-01-09242, by Dynasty Foundation and Simons–IUM fellowship. T.W. and M.Ž. have been partially supported by the Swiss National Science Foundation, grant 200021_150012, and the SwissMAP NCCR funded by the Swiss National Science Foundation. Results of Appendix A with a sketch of independent proof of the main Theorem 2 have been obtained under support of the RSF grant No. 16-11-10160.

Publisher Copyright:
© 2016


  • Graph complexes

ASJC Scopus subject areas

  • Mathematics (all)


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