Pseudo-Anosov subgroups of fibered 3-manifold groups
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Bibliographic record
Abstract
Let S be a hyperbolic surface and let \mathring{S} be the surface obtained from S by removing a point. The mapping class groups \mathrm {Mod}(S) and \mathrm {Mod}(\mathring{S}) fit into a short exact sequence 1 \to \pi_1(S) \to \mathrm {Mod}(\mathring{S}) \to \mathrm {Mod}(S) \to 1. If M is a hyperbolic 3 -manifold that fibers over the circle with fiber S , then its fundamental group fits into a short exact sequence 1 \to \pi_1(S) \to \pi_1(M) \to \mathbb Z \to 1 that injects into the one above. We show that, when viewed as subgroups of \mathrm {Mod} (\mathring{S}) , finitely generated purely pseudo-Anosov subgroups of \pi_1(M) are convex cocompact in the sense of Farb and Mosher. More generally, if we have a \delta -hyperbolic surface group extension 1 \to \pi_1(S) \to \Gamma_\Theta \to \Theta \to 1, any quasiisometrically embedded purely pseudo-Anosov subgroup of \Gamma_\Theta is convex cocompact in \mathrm {Mod}(\mathring{S}) . We also obtain a generalization of a theorem of Scott and Swarup by showing that finitely generated subgroups of \pi_1(S) are quasiisometrically embedded in hyperbolic extensions \Gamma_\Theta .
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| 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