Henry Segerman (UT Austin)


Ideal triangulations and components of the character variety


There is a natural map from a deformation variety of a manifold to its character variety, which builds a representation from the shapes of ideal hyperbolic tetrahedra given by a point in the deformation variety. The Dehn surgery component of the character variety is always in the image of this map. We don't know much in general about other components of the character variety, and if or when the deformation variety maps to them.
I will talk about a concrete example for which the triangulation matters as to which components of the character variety a given deformation variety of the manifold maps to, and discuss a potential way to get around this dependence on the triangulation.

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Please send comments to Shelly Harvey ().