Conjecture 4.2 — The classes µi are non-trivial for all i = 1, 2,···.

Definitions and mathematical statement

Let $\mu_i$ be the classes defined in the preceding source construction, and let $A_i$ be their respective ambient groups. Conjecture 4.2 asserts \[ \forall i\in{\mathbb{Z}}_{\geq1},\qquad\mu_i\ne0\text{ in }A_i. \] The excerpt supplies neither the construction of these classes nor their degrees, homology/cohomology theory, coefficients, ambient spaces or groups, genus/rank conditions, or stabilization conventions. The registry identifies them as Morita's classes, but that name does not determine the omitted data.

The universal positive-index nonvanishing assertion is retained, without replacing the classes by another familiar characteristic-class family. The sentence "More generally we have the following" announces an omitted extension; no algebraic independence, product-nonvanishing or other stronger statement is inferred. The registry reports partial nontriviality results without specifying which indices or references.

Short English statement

Every class $\mu_i$, $i\geq1$, in the source's undefined family is conjectured nonzero. Its construction, target groups and reported partial results are missing.

Sources

• Local registry: data/unsolvedmath/problems.json, permanent UnsolvedMath ID $11000309$, exact source code catalogue entry.
• Farb, Problems on Mapping Class Groups and Related Topics, Conjecture 4.2, PDF page 365: 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.
• The registry calls these Morita's $\mu_i$ classes and mentions partial nonvanishing without any exact primary citation. The preceding construction and following generalization are absent.