Homological Computability of Restricted Singularity Classes

Definitions and mathematical statement

The supplied record concerns a class $W$ of smooth maps to the plane, written schematically as $f\colon M\to{\mathbb{R}}^2$. Here $M$ denotes the source manifold; its dimension, boundary conditions, compactness assumptions, and any additional structure are not specified. The record describes $W$ by excluding certain singularity types of these maps and certain singular features in the target, but does not identify the exclusions or give a complete definition of $W$.

The recorded question is: Why is the class $W$ homologically computable? The meaning of "homologically computable," the homological object to be computed, and the hypotheses and quantifiers of a proposed mathematical assertion are not supplied. Consequently, this question cannot be promoted to a precise theorem or conjecture from the supplied material.

The supplied statement-verification note describes the question as a rhetorical transition in the report, immediately followed by an explanation of homological computability, and marks the statement as unrecoverable. This qualification must be retained alongside the registry's supplied open label; neither label establishes a verified unresolved mathematical problem.

Short English statement

The record asks for a homological explanation of a class $W$ of smooth maps to the plane defined through unspecified singularity exclusions. Its definition and the intended meaning of homological computability are missing. Supplied verification describes the question as rhetorical and already explained in its source, so no precise independent open problem is recoverable here.

Sources

• Local UnsolvedMath registry, data/unsolvedmath/problems.json, permanent ID $30001797$, source code catalogue entry, title "Homological Computability of Restricted Singularity Classes." The supplied record belongs to the Oberwolfach Reports Open Problems collection and gives proposed year 2011; no individual proposer is identified.
• Supplied report citation: New Directions in Algebraic $K$-Theory (2011), Oberwolfach Reports, pp. 1469--1509, DOI 10.4171/owr/2011/27. Supplied source URL and literature-source link labeled "original question": https://doi.org/10.4171/owr/2011/27. The collection describes these reports as documenting mathematical workshops and their open-problem discussions. No specific page or complete contextual passage for this question is supplied.
• Supplied literature assessment, checked on 2026-08-21: status open; the extracted question asks for a homological explanation of the definition of $W$, with insufficient context to identify a resolving theorem. This is supplied dated curation derived from the OWR collection, not independently verified here; time-sensitive status and cited claims require independent verification.
• Supplied statement-verification qualification: the official report is described as posing the question rhetorically and immediately explaining homological computability of the class of maps. The registry marks the statement unrecoverable, promotes no separate clean statement, and retains the original record for provenance. This source characterization has not been independently verified here.