247 research outputs found
Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties
The space AH(M) of marked hyperbolic 3-manifold homotopy equivalent to a
compact 3-manifold with boundary M sits inside the PSL_2(C)-character variety
X(M) of \pi_1(M). We study the dynamics of the action of Out(\pi_1(M)) on both
AH(M) and X(M). The nature of the dynamics reflects the topology of M.
The quotient AI(M)=AH(M)/Out(\pi_1(M)) may naturally be thought of as the
moduli space of unmarked hyperbolic 3-manifolds homotopy equivalent to M and
its topology reflects the dynamics of the action
Infinitesimal rigidity of a compact hyperbolic 4-orbifold with totally geodesic boundary
Kerckhoff and Storm conjectured that compact hyperbolic n-orbifolds with
totally geodesic boundary are infinitesimally rigid when n>3. This paper
verifies this conjecture for a specific example based on the 4-dimensional
hyperbolic 120-cell.Comment: 9 page
Local rigidity of hyperbolic manifolds with geodesic boundary
Let W be a compact hyperbolic n-manifold with totally geodesic boundary. We
prove that if n>3 then the holonomy representation of pi_1 (W) into the
isometry group of hyperbolic n-space is infinitesimally rigid.Comment: 30 page
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