De la topologie des courbes sur les surfaces aux cartes unicellulaires

Abstract : This thesis stay in between topology and combinatory. Our first concerned is the problem of realization of dual unit ball of intersection norms on orientable surfaces. We also show a certain relation between intersection norms and Thurston norms on 3-manifolds. On the other part, we show the existence of graph structure on unicellular maps on orientable surface coming from a surgery operation on unicellular maps: a surgery graph. Its happen that surgery graph on unicellular collections and cubic unicellular maps is connected.
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Abdoul Karim Sane. De la topologie des courbes sur les surfaces aux cartes unicellulaires. Topologie générale [math.GN]. Université de Lyon, 2019. Français. ⟨NNT : 2019LYSEN028⟩. ⟨tel-02446574v1⟩

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