Tropical curves, graph complexes, and top weight cohomology of Mg

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Tropical curves, graph complexes, and top weight cohomology of Mg. / Chan, Melody; Galatius, Søren; Payne, Sam.

In: Journal of the American Mathematical Society, Vol. 34, No. 2, 2021, p. 565-594.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Chan, M, Galatius, S & Payne, S 2021, 'Tropical curves, graph complexes, and top weight cohomology of Mg', Journal of the American Mathematical Society, vol. 34, no. 2, pp. 565-594. https://doi.org/10.1090/jams/965

APA

Chan, M., Galatius, S., & Payne, S. (2021). Tropical curves, graph complexes, and top weight cohomology of Mg. Journal of the American Mathematical Society, 34(2), 565-594. https://doi.org/10.1090/jams/965

Vancouver

Chan M, Galatius S, Payne S. Tropical curves, graph complexes, and top weight cohomology of Mg. Journal of the American Mathematical Society. 2021;34(2):565-594. https://doi.org/10.1090/jams/965

Author

Chan, Melody ; Galatius, Søren ; Payne, Sam. / Tropical curves, graph complexes, and top weight cohomology of Mg. In: Journal of the American Mathematical Society. 2021 ; Vol. 34, No. 2. pp. 565-594.

Bibtex

@article{343c99e4fbf445f2aab0f69518b7facf,
title = "Tropical curves, graph complexes, and top weight cohomology of Mg",
abstract = "We study the topology of a space parametrizing stable tropical curves of genus g with volume 1, showing that its reduced rational homology is canonically identified with both the top weight cohomology of M_g and also with the genus g part of the homology of Kontsevich's graph complex. Using a theorem of Willwacher relating this graph complex to the Grothendieck-Teichmueller Lie algebra, we deduce that H^{4g-6}(M_g;Q) is nonzero for g=3, g=5, and g at least 7. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. We also give an independent proof of another theorem of Willwacher, that homology of the graph complex vanishes in negative degrees.",
author = "Melody Chan and S{\o}ren Galatius and Sam Payne",
year = "2021",
doi = "10.1090/jams/965",
language = "English",
volume = "34",
pages = "565--594",
journal = "Journal of the American Mathematical Society",
issn = "0894-0347",
publisher = "American Mathematical Society",
number = "2",

}

RIS

TY - JOUR

T1 - Tropical curves, graph complexes, and top weight cohomology of Mg

AU - Chan, Melody

AU - Galatius, Søren

AU - Payne, Sam

PY - 2021

Y1 - 2021

N2 - We study the topology of a space parametrizing stable tropical curves of genus g with volume 1, showing that its reduced rational homology is canonically identified with both the top weight cohomology of M_g and also with the genus g part of the homology of Kontsevich's graph complex. Using a theorem of Willwacher relating this graph complex to the Grothendieck-Teichmueller Lie algebra, we deduce that H^{4g-6}(M_g;Q) is nonzero for g=3, g=5, and g at least 7. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. We also give an independent proof of another theorem of Willwacher, that homology of the graph complex vanishes in negative degrees.

AB - We study the topology of a space parametrizing stable tropical curves of genus g with volume 1, showing that its reduced rational homology is canonically identified with both the top weight cohomology of M_g and also with the genus g part of the homology of Kontsevich's graph complex. Using a theorem of Willwacher relating this graph complex to the Grothendieck-Teichmueller Lie algebra, we deduce that H^{4g-6}(M_g;Q) is nonzero for g=3, g=5, and g at least 7. This disproves a recent conjecture of Church, Farb, and Putman as well as an older, more general conjecture of Kontsevich. We also give an independent proof of another theorem of Willwacher, that homology of the graph complex vanishes in negative degrees.

U2 - 10.1090/jams/965

DO - 10.1090/jams/965

M3 - Journal article

VL - 34

SP - 565

EP - 594

JO - Journal of the American Mathematical Society

JF - Journal of the American Mathematical Society

SN - 0894-0347

IS - 2

ER -

ID: 257967125