Simpler Quantization of Weil-Petersson Iterated Fibrations

Definitions and mathematical statement

Qualified construction problem. The supplied record asks for a simpler construction and quantization of the iterated fibration structure used for the Weil--Petersson metric and its associated pseudodifferential calculus.

Here the Weil--Petersson metric, the iterated fibration structure, and the associated pseudodifferential calculus designate the objects referred to in the supplied source record. The record does not specify the underlying space, its parameters, its compactification or boundary geometry, the fibrations and their compatibility conditions, the operator or symbol classes, or the meaning and required properties of quantization in this setting. It also gives no reference construction or criterion for comparing simplicity.

Subject to these unresolved specifications, the requested task is: construct the intended iterated fibration structure and its quantization by a simpler method, retaining the properties needed for the intended Weil--Petersson pseudodifferential calculus. The supplied record does not identify those properties, so this remains a qualified research request rather than a fully specified mathematical existence statement. No particular domain, boundary condition, or universal quantifier over geometric parameters can be inferred from the record.

Short English statement

Find a simpler way to construct and quantize the iterated fibration structure associated with the Weil--Petersson metric and its pseudodifferential calculus. The intended geometric setting, required properties, and meaning of "simpler" are unspecified and require human mathematical review.

Sources

• Local UnsolvedMath problem registry, permanent ID $30004704$, source problem code catalogue entry; supplied complete source record, titled "Simpler Quantization of Weil-Petersson Iterated Fibrations." The record belongs to the Oberwolfach Reports Open Problems collection. No individual proposer is supplied; the proposed year is recorded as 2021.
• Supplied report citation: Analysis, Geometry and Topology of Singular PDE (2022), Oberwolfach Reports, DOI 10.4171/owr/2021/27, pp. 1407--1461. Supplied source URL and literature-source link, labeled "Oberwolfach report": https://doi.org/10.4171/owr/2021/27. The background describes Oberwolfach Reports as documenting mathematical workshops and their open-problem discussions. The report text and a pinpoint location for this question were not supplied, and the cited source has not been independently consulted here.
• Supplied literature assessment, checked on 2026-08-22: the record labels the problem open and states that the extracted request for a simpler method is underspecified, while the report presents techniques rather than a definitive simplification. This is supplied dated curation, not an independently verified literature assessment or mathematical conclusion. The background explicitly calls for independent verification of time-sensitive status and cited claims.
• The registry labels the statement corrected_verified and records a manual semantic, typographic, and LaTeX review claiming that the clean statement is self-contained and preserves the target without unsupported additions. This is a supplied editorial assessment; it does not resolve the missing mathematical specifications listed above.