Differentials on graph complexes II: hairy graphs

Anton Khoroshkin, Thomas Willwacher, Marko Živković

Research output: Contribution to journalArticlepeer-review


We study the cohomology of the hairy graph complexes which compute the rational homotopy of embedding spaces, generalizing the Vassiliev invariants of knot theory. We provide spectral sequences converging to zero whose first pages contain the hairy graph cohomology. Our results yield a way to construct many nonzero hairy graph cohomology classes out of (known) non-hairy classes by studying the cancellations in those sequences. This provide a first glimpse at the tentative global structure of the hairy graph cohomology.

Original languageEnglish
Pages (from-to)1781-1797
Number of pages17
JournalLetters in Mathematical Physics
Issue number10
StatePublished - 1 Oct 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017, Springer Science+Business Media Dordrecht.


  • Embedding calculus
  • Graph complexes
  • Operads

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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