Joan Porti – Conway spheres detected by ideal points of the character variety

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Date(s) - 6 mai 2011

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This is joint work with Luisa Paoluzzi. In the 80’s Culler and Shalen found a method to construct essential surfaces from the ideal points of the variety of characters. In this talk I will review this theory and i will sketch the proof of the following theorem: the Conway spheres of a Bonahon-Siebemann decomposition of a hyperbolic link are surfaces associated to ideal points. Here a Bonahon-Siebemann decomposition is the orbifold analogue of the JSJ splitting, by considering orbifolds on the three sphere with branching locus this link. For instance, this occurs when the link has a unique Conway sphere.