Conjecture 6.1 — The classes e1,t 3,t 5,··· are all non-trivial.

Definitions and mathematical statement

Retain the source Lie algebra $\mathfrak h_{g,1}^{{\mathbb{Q}}}$, its symplectic-group action $\operatorname{Sp}$, and the classes \[ e_1,t_3,t_5,\ldots\ \in\ V_g=H^2(\mathfrak h_{g,1}^{{\mathbb{Q}}};{\mathbb{Q}})^{\operatorname{Sp}}. \] Here the superscript denotes invariant classes in Lie-algebra cohomology. The precise Lie algebra, coefficient convention, cochain/support convention and class constructions occur in missing preceding text; the usual symplectic-derivation interpretation is not imposed as a replacement definition.

The conjecture asserts all of these classes are nonzero, linearly independent and span $V_g$. In an ordinary vector-space basis interpretation, every relation \[ a_0e_1+\sum_{j=1}^{r}a_jt_{2j+1}=0, \qquad a_j\in{\mathbb{Q}}, \] has all coefficients zero, and every class in $V_g$ is a finite such linear combination. If a completed/continuous cohomology or a weightwise stable interpretation is intended, the corresponding meaning of basis must instead be specified. The source does not give a genus range or say whether the claim is for fixed $g$ or the stable limit. No formula for the unnamed classes or partial nonvanishing result is invented.

Short English statement

The source conjectures that $e_1,t_3,t_5,\ldots$ are nonzero and form a basis of the symplectic-invariant second cohomology of the indicated Lie algebra, with genus and completion conventions unresolved.

Sources

• Problems on Mapping Class Groups and Related Topics, edited by Farb, Conjecture 6.1, supplied PDF page 371. https://www.math.uchicago.edu/~farb/papers/mcgbook.pdf. Recorded access 2026-07-29; extraction pdf-font-structure. The preceding Lie-algebra and class definitions are absent.
• Local UnsolvedMath registry, data/unsolvedmath/problems.json, permanent ID $11000318$, exact source code catalogue entry; supplied OPEN-TRIAGE summary mentions partial Morita-type nontriviality without a precise theorem or bibliography.