Problem 2.3 — Find a similar geometric interpretation for the irreducible constituents for compact nonabelian groups G.

Definitions and mathematical statement

Problem 2.3 asks, for compact nonabelian groups $G$, for a geometric interpretation of the source's irreducible constituents similar to an interpretation given previously. A constituent means an irreducible component or factor of a specified representation in its specified decomposition category. The supplied excerpt gives neither that representation nor its acting group, coefficient space, decomposition, or earlier geometric model.

Consequently the retained request is to geometrically realize or describe the irreducible pieces of the source construction associated with compact nonabelian $G$, in the same sense as the omitted preceding case. It is not established here that the constituents are representations of $G$ itself rather than of a mapping class group acting on an object built from $G$. Nor does the excerpt restrict $G$ to connected compact Lie groups or specify finite-dimensional, unitary, discrete-sum or direct-integral conventions.

A complete mathematical formulation must recover the representation, the irreducibility category, the geometric objects and their relation to the constituents before an analogue can be stated. No particular character variety, quantization or Peter--Weyl construction is selected from the wording alone.

Short English statement

For compact nonabelian $G$, find the analogue of the omitted geometric interpretation of certain irreducible constituents. The representation, acting group and preceding model are missing.

Sources

• Local registry: data/unsolvedmath/problems.json, permanent UnsolvedMath ID $11000189$, exact source code catalogue entry.
• Farb, Problems on Mapping Class Groups and Related Topics, Problem 2.3, PDF page 216: https://www.math.uchicago.edu/~farb/papers/mcgbook.pdf. Supplied access date: 2026-07-29; extraction: pdf-font-structure; repeated local numbering disambiguated by page among 329 headings.
• No preceding representation or geometric construction, individual attribution, or additional primary citation is supplied. The registry explicitly cannot verify the literature status.