Big Torelli groups: generation and commensuration
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Bibliographic record
Abstract
For any surface \Sigma of infinite topological type, we study the Torelli subgroup \mathcal I(\Sigma) of the mapping class group MCG (\Sigma) , whose elements are those mapping classes that act trivially on the homology of \Sigma . Our first result asserts that {\mathcal I}(\Sigma) is topologically generated by the subgroup of MCG (\Sigma) consisting of those elements in the Torelli group which have compact support. Next, we prove the abstract commensurator group of {\mathcal I}(\Sigma) coincides with MCG (\Sigma) . This extends the results for finite-type surfaces [9, 6, 7, 16] to the setting of infinite-type surfaces.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it