# Character varieties of higher dimensional representations and splittings of 3-manifolds

@article{Hara2014CharacterVO, title={Character varieties of higher dimensional representations and splittings of 3-manifolds}, author={Takashi Hara and Takahiro Kitayama}, journal={Geometriae Dedicata}, year={2014}, volume={213}, pages={433-466} }

In 1983 Culler and Shalen established a way to construct essential surfaces in a 3-manifold from ideal points of the $$\mathrm {SL}_2$$ SL 2 -character variety associated to the 3-manifold group. We present in this article an analogous construction of certain kinds of branched surfaces (which we call essential tribranched surfaces ) from ideal points of the $$\mathrm {SL}_n$$ SL n -character variety for a natural number n greater than or equal to 3. Further we verify that such a branched…

## 3 Citations

Representation varieties detect essential surfaces

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- 2016

Extending Culler-Shalen theory, Hara and the second author presented a way to construct certain kinds of branched surfaces in a $3$-manifold from an ideal point of a curve in the…

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Extending Culler-Shalen theory, Hara and the second author presented a way to construct certain kinds of branched surfaces in a $3$-manifold from an ideal point of a curve in the…

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