Quantum hyperbolic Dehn-filling convergence conjecture

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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 n→∞n\to\infty,

HN(Wn,Ln,ρn)2N⟶HN(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.

References

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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