Differentials on graph complexes II: hairy graphs

Anton Khoroshkin; Thomas Willwacher; Marko Živković

doi:10.1007/s11005-017-0964-9

Differentials on graph complexes II: hairy graphs

Anton Khoroshkin, Thomas Willwacher, Marko Živković

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	1781-1797
Number of pages	17
Journal	Letters in Mathematical Physics
Volume	107
Issue number	10
DOIs	https://doi.org/10.1007/s11005-017-0964-9
State	Published - 1 Oct 2017
Externally published	Yes

Bibliographical note

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

Keywords

Embedding calculus
Graph complexes
Operads

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s11005-017-0964-9

Cite this

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keywords = "Embedding calculus, Graph complexes, Operads",

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KW - Operads

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Differentials on graph complexes II: hairy graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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