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Benjamin Audoux

Applications de modèles combinatoires issus de la topologie

_Along its development, topology set up several combinatorial models, and unexpected applications can emerge from them. They can indeed be developped by their own, and then reused in other context, related to topology or not. In a first part we develop a, so-called welded, combinatorial theory which extend the combinatorics of link diagrams and then use it to classify properly embedded annuli in B4 up to link-homotopy. In a second part, we take advantage of a reformulation of CSS error-correcting quantum codes in terms of chain complexes to define a product notion for these codes and give a criterion which provides a control on the minimum distance of the product of two codes. Then we study several families of codes for which the criterion can be efficiently applied.

_- habilitation of Aix-Marseille Université
_- defended on february 16th, 2018 with hebilitation committee
_M. Boileau Aix-Marseille Université Tutor
_S. Kamada Osaka City University Referee
_D. Kohel Aix-Marseille Université Committee member
_C. Lescop Université de Grenoble-Alpes Chairman
_P. Teichner Max Planck Institute Referee
_J-P. Tillich INRIA de Paris Committee member


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