Kapovich's unknotted Menger-curve and hyperbolic-quotient conjecture
Kapovich's unknotted Menger-curve and hyperbolic-quotient conjecture
Let be the hyperbolic group with boundary the Menger curve, and let be Granier's discrete, convex-cocompact, faithful representation. Write for the limit set of , let be the standard Menger curve in , and let be the domain of discontinuity. Kapovich's conjecture. The limit set is ambient-isotopic to in , and the quotient 3-manifold is hyperbolic. The paper's abstract states that it proves the hyperbolicity assertion in the corresponding orbifold setting, while the supplied text does not state a resolution of the unknottedness assertion.
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Sources & referencesView supporting material
Primary source
Jiming Ma and Baohua Xie, “Menger curve and Spherical CR uniformization of a closed hyperbolic 3-orbifold”, arXiv:2201.04765 (2024).
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