The variety of characters in PSL(2,C)

By M. Heusener, J. Porti. 2003

62 citations recorded by the source corpus.

We study some basic properties of the variety of characters in PSL(2,C) of a finitely generated group. In particular we give an interpretation of its points as characters of representations. We construct 3-manifolds whose variety of characters has arbitrarily many components that do not lift to SL(2,C). We also study the singular locus of the variety of characters of a free group.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8d24ad09fef21bba4a61e06d9c7a70f842ab5e63

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. J. Porti
2. P. Menal-Ferrer

In Geometry and Topology

1. J. Porti
2. P. Menal-Ferrer
3. M. Heusener
4. B. Leeb
5. Michael Kapovich
6. Anna Wienhard

In Mathematical Physics

1. J. Porti
2. P. Menal-Ferrer
3. B. Leeb
4. Michael Kapovich
5. Anna Wienhard

Citations in the corpus

• Deformations of reducible representations of 3–manifold groups into PSL2(ℂ) (2004, background): “ed characters Let α: π1(M) →C∗ be a representation such that α is a simple zero of the Alexander invariant. Moreover, we shall suppose in this section that χα: π1(M) →R is real valued. We recall from [HP04] that the character χρ of a representation ρ∈ R(M) maps γ∈π1(M) to χρ(γ) = trace2(ρ(γ)). 10.1 ”
• Twisted cohomology for hyperbolic three manifolds (2010, background): “ntinuously the cone angle. The mapX(M,SL(2,C)) → X(M,PSL(2,C)) is a local homeomorphismexcept at characters of reducible representations or representations that preserve a (unoriented) geodesic of H3 [13]. Thus we get a continuous path of representations in X(M,SL(2,C)) parametrized by the cone angl”