Quantum hyperbolic Dehn-filling convergence conjecture

From papers

Let MM be a cusped manifold, and let (Wn,Ln,ρn)(W_n,L_n,\rho_n) be a sequence of compact hyperbolic Dehn fillings of MM converging geometrically to MM, where LnL_n consists of the simple short geodesics forming the filling cores and ρn\rho_n is the holonomy of WnW_n. Quantum hyperbolic Dehn-filling convergence conjecture. For every fixed NN, as nn\to\infty,

HN(Wn,Ln,ρn)2NHN(M)2N.H_N(W_n,L_n,\rho_n)^{2N} \longrightarrow H_N(M)^{2N}.

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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