Differentials on graph complexes

Anton Khoroshkin; Thomas Willwacher; Marko Živković

doi:https://doi.org/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	American 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

Keywords

Graph complexes

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

https://doi.org/10.1016/j.aim.2016.05.029

Cite this

@article{1e677a910846485195a589ecf49e673a,

title = "Differentials on graph complexes",

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.",

keywords = "Graph complexes",

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

note = "Publisher Copyright: {\textcopyright} 2016",

year = "2017",

month = feb,

day = "5",

doi = "https://doi.org/10.1016/j.aim.2016.05.029",

language = "American English",

volume = "307",

pages = "1184--1214",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Differentials on graph complexes

AU - Khoroshkin, Anton

AU - Willwacher, Thomas

AU - Živković, Marko

PY - 2017/2/5

Y1 - 2017/2/5

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.

KW - Graph complexes

UR - http://www.scopus.com/inward/record.url?scp=85007386838&partnerID=8YFLogxK

U2 - https://doi.org/10.1016/j.aim.2016.05.029

DO - https://doi.org/10.1016/j.aim.2016.05.029

M3 - Article

SN - 0001-8708

VL - 307

SP - 1184

EP - 1214

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Differentials on graph complexes

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this