Author:
Felder Matteo,Naef Florian,Willwacher Thomas
Abstract
AbstractWe study three graph complexes related to the higher genus Grothendieck–Teichmüller Lie algebra and diffeomorphism groups of manifolds. We show how the cohomology of these graph complexes is related, and we compute the cohomology as the genus g tends to $$\infty $$
∞
. As a byproduct, we find that the Malcev completion of the genus g mapping class group relative to the symplectic group is Koszul in the stable limit, partially answering a question of Hain.
Funder
Swiss Federal Institute of Technology Zurich
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy,General Mathematics
Reference36 articles.
1. Alekseev, A., Kawazumi, N., Kuno, Y., Naef, F.: Higher genus Kashiwara–Vergne problems and the Goldman–Turaev Lie bialgebra. C. R. Math. Acad. Sci. Paris 355(2), 123–127 (2017)
2. Alekseev, A., Kawazumi, N., Kuno, Y., Naef, F.: The Goldman–Turaev Lie bialgebra and the Kashiwara–Vergne problem in higher genera (2018). Preprint arXiv:1804.09566
3. Alekseev, A., Torossian, C.: The Kashiwara–Vergne conjecture and Drinfeld’s associators. Ann. of Math. (2) 175(2), 415–463 (2012)
4. Asada, M., Kaneko, M.: On the automorphism group of some pro-$$l$$ fundamental groups. Galois representations and arithmetic algebraic geometry (Kyoto, 1985/Tokyo, 1986). Adv. Stud. Pure Math. 12, 137–159, North-Holland, Amsterdam (1987)
5. Berglund, A.: Koszul spaces. Trans. Am. Math. Soc. 366(9), 4551–4569 (2014)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. On the Cohomology of Torelli Groups. II;International Mathematics Research Notices;2023-07-05
2. On the Torelli Lie algebra;Forum of Mathematics, Pi;2023