Finite Volume Properly Convex Deformations of the Figure-eight Knot

In this paper we show that some open set of the representations of the fundamental group of figure-eight knot complement found in \cite{Ballas12a} are the holonomies of a family of finite volume properly convex projective structures on the figure-eight knot complement.Comment: 21 pages, 7 figure. Incorporated additional referee comments, fixed typos. Simplified the proof of Lemma 3.3. To appear in Geometriae Dedicat

Deformations of Non-Compact, Projective Manifolds

In this paper, we demonstrate that the complete hyperbolic structure of various two-bridge knots and links cannot be deformed to an inequivalent strictly convex projective structure. We also prove a complementary result showing that under certain rigidity hypotheses, branched covers of amphicheiral knots admit non-trivial, strictly convex deformations near their complete hyperbolic structure.Comment: 28 pages, 1 figure corrected typos, added references, incorporated referee suggestions, strengthened conclusion of main result and fixed small gap in its proo