Abstract
In this paper we show that some open set of the representations of the fundamental group of figure-eight knot complement found in Ballas (2014) are the holonomies of a family of finite volume properly convex projective structures on the figure-eight knot complement.
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Acknowledgments
I would like to thank Daryl Cooper for first suggesting that the representations in [1] might correspond to properly convex projective structures and for several helpful conversations throughout this Project. I would also like to acknowledge support from U.S. National Science Foundation Grants DMS 1107452, 1107263, 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network). I would also like to thank the referee for several helpful comments and suggestions including a simplified proof of Lemma 2 and for pointing out an incorrect corollary in a previous version.
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Ballas, S.A. Finite volume properly convex deformations of the figure-eight knot. Geom Dedicata 178, 49–73 (2015). https://doi.org/10.1007/s10711-015-0043-2
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DOI: https://doi.org/10.1007/s10711-015-0043-2