Problem 7.15 — (D.

Definitions and mathematical statement

The source asks for a formulation, attributed to D. Thurston, rather than asserting a specified asymptotic identity: find a correct generalization of the volume conjecture to other noncompact Lie groups. A proposed formulation must specify the noncompact Lie groups under consideration, the knots or manifolds to which it applies, the associated invariants and their asymptotic parameter, and the geometric quantity and normalization to be recovered in the limit. It must also explain in what sense it generalizes the volume conjecture intended in the source. The supplied record gives neither that original formulation nor these additional choices; consequently it does not determine a single quantified conjecture or a particular limiting formula.

Short English statement

D. Thurston asks for a correct version of the volume conjecture for other noncompact Lie groups. The choice of group, invariant, geometric quantity, hypotheses, and limiting procedure is part of the requested work and is not specified in this excerpt.

Sources

• Local UnsolvedMath registry, permanent ID 10400130, source code catalogue entry; supplied title "Problem 7.15 --- (D." and attribution D. Thurston in the statement.
• Ohtsuki, Problems on invariants of knots and 3-manifolds (2002), Problem 7.15, PDF page 111. Supplied URL: https://msp.org/gtm/2002/04/gtm-2002-04-024s.pdf. Recorded access: 2026-07-29; extraction: pdf-font-structure. The collection distinguishes 231 numbered bold problem, conjecture, and question headings from surrounding references to them.
• The supplied record labels the item open and OPEN-TRIAGE, with the assessment "Not obviously resolved." Its status evidence is NEEDS_REVIEW: the 2002 source presents an open problem, and a current primary-literature status audit remains. The publicly accessible author/publisher copy has redistribution terms requiring review.