Incomplete Slice-Missing-Slice-Disc Lead-In

Definitions and mathematical statement

For an integer $n\geq 1$, let $S^n$ denote the standard $n$-sphere and $B^n$ the closed $n$-ball. Set $X=S^1\times B^3$, so that $\partial X=S^1\times S^2$.

The supplied fragment is headed "Problem 3. (Slice missing slice disc problem)." A tentative normalization of its damaged mathematical typography places a knot \[ K\subset S^1\times S^2=\partial(S^1\times B^3). \] It describes $K$ by reference to an unavailable Figure 1 and asserts that $K$ bounds two "obvious ribbon discs" $D_1$ and $D_2$. On the natural reading that these discs lie in $X$, the boundary relations would be \[ \partial D_1=\partial D_2=K. \] This ambient interpretation is provisional: the supplied extraction does not provide a complete specification of the discs, their embedding category, or the convention for "ribbon." No additional ribbon condition is imposed here.

Unresolved mathematical statement. The fragment stops at "such that the simple" before supplying the remaining condition or the question. Figure 1 is absent, and no clean statement is supplied. Consequently, neither the particular knot nor the intended quantified assertion can be recovered from this record. The displayed relations record only a tentative reading of the lead-in; they do not constitute a complete open problem.

Short English statement

The supplied lead-in describes a figure-dependent knot in $S^1\times S^2$ bounding two ribbon discs, apparently in $S^1\times B^3$. Its defining condition and actual question are missing. The registry labels the entry open and its statement unrecoverable; neither label supplies a complete mathematical assertion.

Sources

• Local UnsolvedMath registry, permanent ID $30005377$, source problem code catalogue entry, title "Incomplete Slice-Missing-Slice-Disc Lead-In," in the Oberwolfach Reports Open Problems collection. The supplied fragment identifies itself as Problem 3, "Slice missing slice disc problem." No individual proposer is supplied; the proposed year is 2023.
• Supplied report citation: Low-dimensional Topology (2023), Oberwolfach Reports, pp. 151--213, DOI 10.4171/owr/2023/3. Source URL and literature-source link labelled "original Oberwolfach report": https://doi.org/10.4171/owr/2023/3.
• Supplied literature-source link labelled "Davis--Nagel--Park--Ray, concordance in S1 times S2": https://doi.org/10.1112/jlms.12125. The record supplies no fuller bibliographic citation or precise result connecting this reference to the missing question.
• Supplied literature assessment, checked on 2026-08-22: the extraction ends before its actual condition or question, and the curation reports that literature on slice and ribbon discs in $S^1\times S^2$ does not identify a resolution of this exact fragment; it therefore classifies the entry as open. This is supplied dated curation, not an independently verified literature assessment.
• The supplied statement-verification note reports that the official report confirms this extraction is the first half of a figure-dependent problem and is not independently self-contained. It states that no separate clean statement is promoted and that the original record is retained for provenance. This verification claim is reproduced as supplied, without independent source consultation.