Représentations et Structures Géométriques

Abstract : This memoir consists in a survey of my mathematical works, focusing essentialy on character varieties for fundamental groups of 3-manifolds. Two major influences converge in these researchs : first the study of hyperbolic structures on 3-manifolds (Thurston, Neumann-Zagier...) and second the construction of coordinates for character varieties of fundamental groups of surfaces (Fock-Goncharov...). The tools I (among others) developped may be used for an experimental study of these character va- rieties (through formal computations) as well as a more theoretical treatment. Some ques- tions of a more geometric flavor arise, as e.g. the construction of new geometric structures on 3-manifolds or the study of the discreteness of representations.
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Habilitation à diriger des recherches
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Antonin Guilloux. Représentations et Structures Géométriques. Topologie géométrique [math.GT]. UPMC - Université Paris 6 Pierre et Marie Curie, 2015. ⟨tel-01370296⟩

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