Quantum contextual finite geometries from dessins d’enfants. Michel Planat, Alain Giorgetti, Frédéric Holweck, Metod Saniga To cite this version: Michel Planat, Alain Giorgetti, Frédéric Holweck, Metod Saniga. Quantum contextual finite geome- tries from dessins d’enfants.. 2013. hal-00873461v1 HAL Id: hal-00873461 https://hal.archives-ouvertes.fr/hal-00873461v1 Preprint submitted on 15 Oct 2013 (v1), last revised 4 Sep 2015 (v4) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Quantum contextual finite geometries from dessins d’enfants Michel Planat1, Alain Giorgetti2, Fr´ed´eric Holweck3 and Metod Saniga4 1 Institut FEMTO-ST/MN2S, CNRS, 32 Avenue de l’Observatoire, 25044 Besan¸con, France. E-mail:
[email protected] 2 Institut FEMTO-ST/DISC, Universit´ede Franche-Comt´e, 16 route de Gray, F-25030 Besan¸con, France. E-mail:
[email protected] 3 Laboratoire IRTES/M3M, Universit´ede Technologie de Belfort-Montb´eliard, F-90010 Belfort, France. E-mail:
[email protected] 4 Astronomical Institute, Slovak Academy of Sciences, SK-05960 Tatransk´aLomnica, Slovak Republic. E-mail:
[email protected] Abstract. We point out an explicit connection between graphs drawn on compact Riemann surfaces defined over the field Q¯ of algebraic numbers — so-called Grothendieck’s dessins d’enfants — and a wealth of distinguished point-line configurations.