Quantum hyperbolic Dehn-filling convergence conjecture
Quantum hyperbolic Dehn-filling convergence conjecture
Let be a cusped manifold, and let be a sequence of compact hyperbolic Dehn fillings of converging geometrically to , where consists of the simple short geodesics forming the filling cores and is the holonomy of . Quantum hyperbolic Dehn-filling convergence conjecture. For every fixed , as ,
This conjecture proposes continuity of the quantum hyperbolic invariant under geometric convergence of hyperbolic Dehn fillings. The supplied source gives no evidence that it has been resolved.
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Sources & referencesView supporting material
Primary source
S. Baseilhac and R. Benedetti, “Quantum Hyperbolic Invariants Of 3-Manifolds With PSL(2,C)-Characters”, arXiv:math/0306280 (2003).
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