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Dessins for Modular Operad and Grothendieck-Teichmüller Group

Combe, Noémie C. and Manin, Yuri I. and Marcolli, Matilde (2020) Dessins for Modular Operad and Grothendieck-Teichmüller Group. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20210825-184554285

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Abstract

A part of Grothendieck's program for studying the Galois group G_ℚ of the field of all algebraic numbers ℚ emerged from his insight that one should lift its action upon ℚ to the action of G_ℚ upon the (appropriately defined) profinite completion of π₁(ℙ¹∖{0,1,∞}). The latter admits a good combinatorial encoding via finite graphs "dessins d'enfant". This part was actively developing during the last decades, starting with foundational works of A. Belyi, V. Drinfeld and Y. Ihara. Our brief note concerns another part of Grothendieck program, in which its geometric environment is extended to moduli spaces of algebraic curves, more specifically, stable curves of genus zero with marked/labelled points. Our main goal is to show that dual graphs of such curves may play the role of "modular dessins" in an appropriate operadic context.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/2006.13663arXivDiscussion Paper
Additional Information:N. C. Combe acknowledges support from the Minerva Fast track grant from the Max Planck Institute for Mathematics in the Sciences, in Leipzig. M. Marcolli acknowledges support from NSF grant DMS-1707882 and NSERC grants RGPIN–2018–04937 and RGPAS–2018–522593.
Funders:
Funding AgencyGrant Number
Max Planck Institute for Mathematics in the SciencesUNSPECIFIED
NSFDMS-1707882
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPIN-2018-04937
Natural Sciences and Engineering Research Council of Canada (NSERC)RGPAS-2018-522593
Record Number:CaltechAUTHORS:20210825-184554285
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210825-184554285
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110540
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:25 Aug 2021 22:21
Last Modified:25 Aug 2021 22:21

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