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… 
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References

SHOWING 1-10 OF 35 REFERENCES
Representation varieties detect essential surfaces
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
On Culler-Shalen seminorms and Dehn filling
If F is a finitely generated discrete group and G a complex algebraic Lie group, the G-character variety of r is an affine algebraic variety whose points correspond to characters of representations
Local coordinates for SL(n,C) character varieties of finite volume hyperbolic 3-manifolds
Given a finite volume hyperbolic 3-manifold, we compose a lift of the holonomy in SL(2,C) with the n-dimensional irreducible representation of SL(2,C) in SL(n,C). In this paper we give local
Degenerations of hyperbolic structures, II: Measured laminations in 3-manifolds
That paper concerned the general theory of groups acting on R-trees and the relationship of these actions to representations into SL2(C). The purpose of the present paper is to develop the
Hyperbolic Manifolds and Discrete Groups
Preface.-Three-dimensional Topology.-Thurston Norm.-Geometry of the Hyperbolic Space.-Kleinian Groups.-Teichmuller Theory of Riemann Surfaces.-Introduction to the Orbifold Theory.-Complex Projective
Metric Spaces of Non-Positive Curvature
This book describes the global properties of simply-connected spaces that are non-positively curved in the sense of A. D. Alexandrov, and the structure of groups which act on such spaces by
Graph manifolds with boundary are virtually special
Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in π1M, and that the double cosets for crossing surfaces are also separable. We
A basic course in algebraic topology
1: Two-Dimensional Manifolds. 2: The Fundamental Group. 3: Free Groups and Free Products of Groups. 4: Seifert and Van Kampen Theorem on the Fundamental Group of the Union of Two Spaces.
Twisted cohomology for hyperbolic three manifolds
For a complete hyperbolic three manifold M, we consider the representations of its fundamental group obtained by composing a lift of the holonomy with complex finite dimensional representations of
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