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Spherical CR uniformization of Dehn surgeries of the Whitehead link complement Acosta, Miguel in Geometry and Topology (2019), 23(5), 25932664 We apply a spherical CR Dehn surgery theorem in order to obtain infinitely many Dehn surgeries of the Whitehead link complement that carry spherical CR structures. We consider as a starting point the ... [more ▼] We apply a spherical CR Dehn surgery theorem in order to obtain infinitely many Dehn surgeries of the Whitehead link complement that carry spherical CR structures. We consider as a starting point the spherical CR uniformization of the Whitehead link complement constructed by Parker and Will, using a Ford domain in the complex hyperbolic plane H2C. We deform the Ford domain of Parker and Will in H2C in a one-parameter family. On one side, we obtain infinitely many spherical CR uniformizations on a particular Dehn surgery on one of the cusps of the Whitehead link complement. On the other side, we obtain spherical CR uniformizations for infinitely many Dehn surgeries on the same cusp of the Whitehead link complement. These manifolds are parametrized by an integer n≥4, and the spherical CR structure obtained for n=4 is the Deraux–Falbel spherical CR uniformization of the figure eight knot complement. [less ▲] Detailed reference viewed: 132 (2 UL)Character varieties for real forms Acosta, Miguel in Geometriae Dedicata (2019) Let $\Gamma$ be a finitely generated group and G a real form of SL(n,C). We propose a definition for the G-character variety of $\Gamma$ as a subset of the SL(n,C)-character variety of $\Gamma$. We ... [more ▼] Let $\Gamma$ be a finitely generated group and G a real form of SL(n,C). We propose a definition for the G-character variety of $\Gamma$ as a subset of the SL(n,C)-character variety of $\Gamma$. We consider two anti-holomorphic involutions of the SL(n,C)-character variety and show that an irreducible representation with character fixed by one of them is conjugate to a representation taking values in a real form of SL(n,C). We study in detail an example: the SL(n,C), SU(2,1) and SU(3) character varieties of the free product Z/3Z*Z/3Z. [less ▲] Detailed reference viewed: 40 (1 UL)Spherical CR Dehn surgeries Acosta, Miguel in Pacific Journal of Mathematics (2016), 284(2), 257-282 Consider a three dimensional cusped spherical CR manifold M and suppose that the holonomy representation of $\pi_1(M)$ can be deformed in such a way that the peripheral holonomy is generated by a non ... [more ▼] Consider a three dimensional cusped spherical CR manifold M and suppose that the holonomy representation of $\pi_1(M)$ can be deformed in such a way that the peripheral holonomy is generated by a non-parabolic element. We prove that, in this case, there is a spherical CR structure on some Dehn surgeries of M. The result is very similar to R. Schwartz's spherical CR Dehn surgery theorem, but has weaker hypotheses and does not give the uniformizability of the structure. We apply our theorem in the case of the Deraux-Falbel structure on the Figure Eight knot complement and obtain spherical CR structures on all Dehn surgeries of slope $-3 + r$ for $r \in \mathbb{Q}^{+}$ small enough. [less ▲] Detailed reference viewed: 52 (1 UL) |
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