- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:01
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
9
2015
1
Dynamics on the PSL(2, $\mathbb C$)-character variety of a twisted $I$-bundle
Michelle
Lee
University of Michigan, ANN ARBOR, UNITED STATES
Twisted interval bundle, hyperbolic 3-manifold, character variety, outer automorphism group
Let $M$ be a twisted interval bundle over a closed nonorientable hyperbolizable surface. Let $\mathcal{X}(M)$ be the PSL(2, $\mathbb C$)-character variety of $\pi_1(M)$. We examine the dynamics of the action of Out$(\pi_1(M))$ on $\mathcal{X}(M),$ 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$(\pi_1(M))$ on $\mathcal{X}(M)$.
Manifolds and cell complexes
187
201
10.4171/GGD/310
http://www.ems-ph.org/doi/10.4171/GGD/310