52,467 research outputs found
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
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