Geodesic
Dynamics on the PSL(2, $\mathbb C$)-character variety of a twisted $I$-bundle
Michelle Lee1
1University of Michigan, Ann Arbor, USA
Groups, geometry, and dynamics, Tome 9 (2015) no. 1, pp. 187-201

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DOI

Let M be a twisted interval bundle over a closed nonorientable hyperbolizable surface. Let X(M) be the PSL(2, C)-character variety of π1​(M). We examine the dynamics of the action of Out(π1​(M)) on X(M), and in particular, we find an open set on which the action is properly discontinuous that is strictly larger than the interior of the deformation space of marked hyperbolic 3-manifolds homotopy equivalent to M. Furthermore, we identify which discrete and faithful representations can lie in a domain of discontinuity for the action of Out(π1​(M)) on X(M).
DOI : 10.4171/ggd/310
Classification : 57-XX
Mots-clés : Twisted interval bundle, hyperbolic 3-manifold, character variety, outer automorphism group

Michelle Lee  1

1 University of Michigan, Ann Arbor, USA 
Michelle Lee. Dynamics on the PSL(2, $\mathbb C$)-character variety of a twisted $I$-bundle. Groups, geometry, and dynamics, Tome 9 (2015) no. 1, pp. 187-201. doi: 10.4171/ggd/310
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     title = {Dynamics on the {PSL(2,} $\mathbb C$)-character variety of a twisted $I$-bundle},
     journal = {Groups, geometry, and dynamics},
     pages = {187--201},
     year = {2015},
     volume = {9},
     number = {1},
     doi = {10.4171/ggd/310},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/310/}
}
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