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Original Articles

Deformation Spaces of Discrete Groups of SU(2,1) in Quaternionic Hyperbolic Plane: A Case Study

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References

  • [Acosta 16] M. Acosta. “Spherical CR Dehn Surgeries.” Pac. J. Math. 284 (2016),257–282.
  • [Ballas and Long 15] S. Ballas and D. D. Long. “Constructing Thin Subgroups Commensurable with the Figure-Eight Knot Group.” Algebr. Geom. Topol. 15:5 (2015), 3011–3024.
  • [Abdelghani and Heusener 17] L. B. Abdelghani and M. Heusener. “Irreducible Representations of Knot Groups into SL(n,ℂ).” Publ. Mat. 61:2 (2017), 363–394.
  • [Cao and Gongopadhyay 12] W. Cao and K. Gongopadhyay. “Algebraic Characterization of Isometries of the Complex and the Quaternionic Hyperbolic Planes.” Geom. Dedicata 157 (2012), 23–39.
  • [Deraux 15] M. Deraux. “On Spherical CR Uniformization of 3-Manifolds.” Exp. Math. 24:3 (2015), 355–370.
  • [Deraux 16] M. Deraux. “A 1-Parameter Family of Spherical CR Uniformizations of the Figure Eight Knot Complement.” Geom. Topol. 20:6 (2016), 3571–3621.
  • [Falbel 16] E. Falbel, A. Guilloux, P.-V. Koseleff, F. Rouillier, and M. Thistlethwaite. “Character Varieties for SL(3,ℂ): The Figure Eight Knot.” Exp. Math. 25:2 (2016), 219–235.
  • [Falbel 15] E. Falbel, P.-V. Koseleff, and F. Rouillier. “Representations of Fundamental Groups of 3-Manifolds into PGL(3,ℂ): Exact Computations in Low Complexity.” Geom. Dedicata 177 (2015), 229–255.
  • [Falbel 08] E. Falbel. “A Spherical CR Structure on the Complement of the Figure Eight Knot with Discrete Holonomy.” J. Differ. Geom. 79:1 (2008), 69–110.
  • [Goldman and Millson 87] W. M. Goldman and J. J. Millson. “Local Rigidity of Discrete Groups Acting on Complex Hyperbolic Space.” Invent. Math. 88:3 (1987), 495–520.
  • [Goldman 84] W. M. Goldman. “The Symplectic Nature of Fundamental Groups of Surfaces.” Adv. Math. 54:2 (1984), 200–225.
  • [Guilloux and Kim 17] A. Guilloux and I. Kim. Companion Sage Notebook to this Article. Link to the Sage Notebook, 2017.
  • [Guilloux and Will in press] A. Guilloux and P. Will. “On SL(3,C)-Representations of the Whitehead Link Group.” Geom. Dedicata (in press).
  • [Hitchin 92] N. J. Hitchin. “Lie Groups and Teichmüller Space.” Topology 31:3 (1992), 449–473.
  • [Kim and Zhang 18] I. Kim and G. Zhang. “Local Rigidity of Complex Hyperbolic Lattices in Semisimple Lie Groups.” Math. Proc. Camb. Philos. Soc. 165:1 (2018), 179–191.
  • [Kim et al. 12] I. Kim, B. Klingler, and P. Pansu. “Local Quaternionic Rigidity for Complex Hyperbolic Lattices.” J. Inst. Math. Jussieu 11:1 (2012), 133–159.
  • [Kim and Pansu 09] I. Kim and P. Pansu. “Local Rigidity in Quaternionic Hyperbolic Space.” J. Eur. Math. Soc. (JEMS) 11:6 (2009), 1141–1164.
  • [Matsushima and Murakami 63] Y. Matsushima and S. Murakami. “On Vector Bundle Valued Harmonic Forms and Automorphic Forms on Symmetric Riemannian Manifolds.” Ann. Math. (2) 78 (1963), 365–416.
  • [Parker and Will 17] J. R. Parker and P. Will. “A Complex Hyperbolic Riley Slice.” Geom. Topol. 21:6 (2017), 3391–3451.
  • [Raghunathan 65] M. S. Raghunathan. “On the First Cohomology of Discrete Subgroups of Semisimple Lie Groups.” Amer. J. Math. 87 (1965), 103–139.
  • [Schwartz 07] R. E. Schwartz. “Spherical CR Geometry and Dehn Surgery.” In: Annals of Mathematics Studies, vol. 165. Princeton, NJ: Princeton University Press, 2007.
  • [Thurston 83] W. Thurston. “The Geometry and Topology of 3-Manifolds.” Avaialbe online (http://library.msri.org/books/gt3m/), 1983.
  • [Weil 60] A. Weil. “On Discrete Subgroups of Lie Groups.” Ann. Math. (2) 72 (1960), 369–384.

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