Differentials on graph complexes

Anton Khoroshkin; Thomas Willwacher; Marko Živković

doi:10.1016/j.aim.2016.05.029

Differentials on graph complexes

Anton Khoroshkin, Thomas Willwacher, Marko Živković

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

Abstract

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 language	English
Pages (from-to)	1184-1214
Number of pages	31
Journal	Advances in Mathematics
Volume	307
DOIs	https://doi.org/10.1016/j.aim.2016.05.029
State	Published - 5 Feb 2017
Externally published	Yes

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

Keywords

Graph complexes

ASJC Scopus subject areas

Mathematics (all)

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10.1016/j.aim.2016.05.029

Cite this

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abstract = "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.",

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AU - Willwacher, Thomas

AU - Živković, Marko

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N2 - 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.

AB - 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.

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SP - 1184

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Differentials on graph complexes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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