On the Hyperbolic Gluing Equations and Representations of Fundamental Groups of Closed 3-Manifolds

Details On the Hyperbolic Gluing Equations and Representations of Fundamental Groups of Closed 3-Manifolds On the Hyperbolic Gluing Equations and Representations of Fundamental Groups of Closed 3-Manifolds

2010-04-20

arxiv.org/abs/1004.3338v2

Mathematics

Geometric Topology

Scientific paper

We show that for a representation of the fundamental group of a triangulated closed 3-manifold (not necessarily hyperbolic) into $\PSL$ so that any edge loop has non-trivial image under the representation, there exist uncountably many solutions to the hyperbolic gluing equation whose associated representations are conjugate to the given representation, and whose volumes are equal to the volume of the given representation.

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