Question 3 — What can be said about the dimensions of Dλ?

Definitions and mathematical statement

The problem asks to determine the dimensions of the source's family $D_\lambda$, or obtain informative dimension bounds as $\lambda$ varies. Neither $D_\lambda$, its ambient space, the parameter domain nor the meaning of dimension is supplied.

A precise target would be the function $\lambda\mapsto\dim D_\lambda$ in the intended dimension theory. Topological, manifold, algebraic, Hausdorff and vector-space dimensions are not interchangeable, and no one of them can be selected from the notation alone. Consequently no numerical bound, finiteness assertion or guessed geometric interpretation of $D_\lambda$ is added.

Short English statement

Determine the dimension behavior of the missing family $D_\lambda$; its definition and dimension convention are required.

Sources

• Problems on Mapping Class Groups and Related Topics, edited by Farb, Question 3, supplied PDF page 321. https://www.math.uchicago.edu/~farb/papers/mcgbook.pdf. Recorded access 2026-07-29; extraction pdf-font-structure. The preceding definition of $D_\lambda$ and any individual attribution are absent.
• Local UnsolvedMath registry, data/unsolvedmath/problems.json, permanent ID $11000260$, exact source code catalogue entry; supplied OPEN-TRIAGE summary reports unverified status. No additional reference is supplied.