In this paper, we demonstrate that the complete, hyperbolic representation of various two-bridge knot and link groups enjoy a certain local rigidity property inside of the PGL 4 (R) character variety. We also prove a complementary result showing that under certain rigidity hypotheses, branched covers of amphicheiral knots admit non-trivial deformations near… (More)
In this paper we find infinitely many lattices in SL(4, R) each of which contains thin subgroups commensurable with the figure-eight knot group.
Acknowledgments I would like to start by thanking my advisor, Alan Reid, for his patience, encouragement and guidance. I would also like to thank Daryl Cooper, Darren Long, and Jeff Danciger for many helpful conversations. I am grateful to many graduate students for help and support over the year, in particular I would like to thank Sam Taylor. I would like… (More)
In this paper we show that bending a finite volume hyperbolic d-manifold M along a totally geodesic hypersurface Σ results in a properly convex projective structure on M with finite volume. We also discuss various geometric properties of bent manifolds and algebraic properties of their fundamental groups. We then use this result to show in each dimension d… (More)
These notes form a rough outline of the correspondence between the PSL 4 (R)-Hitchin component and convex foliated projective structures from .