For the figure-eight knot complement, the real part of the semi-classical limit of its QHI sequence is rigid and equals 0 or vol(M)/(2 pi) depending on parity of log holonomy eigenvalues on the canonical longitude.
Shalen, Representations of 3–manifold groups , Handbook of geometric topology, North–Holland, Amsterdam (2002) 955–1044
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Volume Conjecture and quantum hyperbolic invariants: the figure eight knot complement
For the figure-eight knot complement, the real part of the semi-classical limit of its QHI sequence is rigid and equals 0 or vol(M)/(2 pi) depending on parity of log holonomy eigenvalues on the canonical longitude.