Deformations of Non-Compact, Projective Manifolds

Abstract

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.

28 pages, 1 figure corrected typos, added references, incorporated referee suggestions, strengthened conclusion of main result and fixed small gap in its proof

References in corpus (2)

• The infinitesimal projective rigidity under Dehn filling
• Collisions at infinity in hyperbolic manifolds

Cited by in corpus (3)

• Finite Volume Properly Convex Deformations of the Figure-eight Knot
• Constructing convex projective 3-manifolds with generalized cusps
• Constructing thin subgroups commensurable with the figure-eight knot group