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

Funding Information:
A.Kh. research has been funded by the Russian Academic Excellence Project ‘5-100’, and has also been partially supported by RFBR Grant 15-01-09242 and by Young Russian Mathematics award. T.W. and M.Ž. have been partially supported by the Swiss National Science foundation, Grant 200021_150012. All three authors have been supported by the SwissMAP NCCR funded by the Swiss National Science foundation.

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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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.",

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

author = "Anton Khoroshkin and Thomas Willwacher and Marko {\v Z}ivkovi{\'c}",

note = "Funding Information: A.Kh. research has been funded by the Russian Academic Excellence Project {\textquoteleft}5-100{\textquoteright}, and has also been partially supported by RFBR Grant 15-01-09242 and by Young Russian Mathematics award. T.W. and M.{\v Z}. have been partially supported by the Swiss National Science foundation, Grant 200021_150012. All three authors have been supported by the SwissMAP NCCR funded by the Swiss National Science foundation. Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media Dordrecht.",

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doi = "10.1007/s11005-017-0964-9",

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AU - Willwacher, Thomas

AU - Živković, Marko

N1 - Funding Information: A.Kh. research has been funded by the Russian Academic Excellence Project ‘5-100’, and has also been partially supported by RFBR Grant 15-01-09242 and by Young Russian Mathematics award. T.W. and M.Ž. have been partially supported by the Swiss National Science foundation, Grant 200021_150012. All three authors have been supported by the SwissMAP NCCR funded by the Swiss National Science foundation. Publisher Copyright: © 2017, Springer Science+Business Media Dordrecht.

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N2 - 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.

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KW - Operads

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JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

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ER -

Differentials on graph complexes II: hairy graphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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