Problem 4.17 — Calculate Wk(M ) for each 3-manifold M.

Definitions and mathematical statement

Problem 4.17 asks to determine \[ W_k(M)\qquad\text{for each }3\text{-manifold }M. \] Here $W_k$ is retained as the source's notation: the supplied extract gives no definition of the object, the index $k$, or any coefficient system. It does not say whether $W_k(M)$ is a module, algebra, homology group, vector space, or numerical invariant, nor provide generators, relations, or a construction. Consequently the problem cannot be converted into a specified calculation by assigning a familiar theory to this symbol.

A complete formulation must recover the definition of $W_k$, the permitted values of $k$ and any parameter dependence, and the intended form of the answer. The source's quantifier ranges over $3$-manifolds without explicit orientability, compactness, connectedness, or boundary assumptions; none is added here. This is a request for computation, not a supplied conjectural equality or classification criterion.

Short English statement

Calculate $W_k(M)$ for every three-manifold. The source extract omits the definition of $W_k$ and the range of $k$, so those missing data must be recovered before the requested calculation has a precise target.

Sources

• Local UnsolvedMath registry, permanent ID $10400095$, exact source code catalogue entry, Problem 4.17. No individual proposer or proposed year is supplied.
• Ohtsuki, Problems on invariants of knots and 3-manifolds (2002), Problem 4.17, PDF page 82: https://msp.org/gtm/2002/04/gtm-2002-04-024s.pdf. Printed bold headings distinguish 231 numbered items from surrounding references.
• Extraction pdf-font-structure, accessed 2026-07-29. Source evidence NEEDS_REVIEW presents an open problem and requires a current primary-literature audit. Research classification OPEN-TRIAGE; the supplied summary calls the all-manifolds computation not obviously resolved. No additional authoritative reference defining $W_k$ is supplied.
• Dataset attribution: Ulam AI / UnsolvedMath Contributors, CC BY 4.0. Source rights NEEDS_REVIEW: publicly accessible author/publisher copy, redistribution terms requiring review.