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dc.contributor.advisor[non identifié]fr
dc.contributor.authorZhang, Jiefr
dc.date.accessioned2014-05-16T16:04:25Z
dc.date.available2014-05-16T16:04:25Z
dc.date.created2011fr
dc.date.issued2011fr
dc.identifier.isbn9780494832851fr
dc.identifier.urihttp://savoirs.usherbrooke.ca/handle/11143/5153
dc.description.abstractWe study in this thesis the cluster category C[subscript S,M] and cluster algebra A[Subscript S,M] of a marked surface (S, M) without punctures. We give a geometric characterization of the indecomposable objects in C[subscript S,M] as homotopy classes of curves in (S, M) and one-parameter families related to non-contractible closed curves in (S , M). Moreover, the Auslander-Reiten structure of the category C[Subscript S,M] is described in geometric terms and we show that the objects without self-extensions in C[Subscript S,M] correspond to curves in (S, M) without self-intersections. As a consequence, we establish that every rigid indecomposable object is reachable from an initial triangulation. As for the cluster algebra A[Subscript S,M], we give a module-theoretic interpretation of Schiffler's expansion formula defined in [42]. Based on the properties of the cluster category C[Subscript S,M], we show the coincidence of Schiffler-Thomas' expansion formula and the cluster character defined in [36].fr
dc.language.isoengfr
dc.publisherUniversité de Sherbrookefr
dc.rights© Jie Zhangfr
dc.titleSur la catégorie amassée d'une surface marquéefr
dc.typeThèsefr
tme.degree.disciplineMathématiquesfr
tme.degree.grantorFaculté des sciencesfr
tme.degree.levelDoctoratfr
tme.degree.namePh.D.fr


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