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Record W2060725822 · doi:10.4171/ggd/302

Pseudo-Anosov subgroups of fibered 3-manifold groups

2014· preprint· en· W2060725822 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueGroups Geometry and Dynamics · 2014
Typepreprint
Languageen
FieldMathematics
TopicGeometric and Algebraic Topology
Canadian institutionsToronto Metropolitan University
FundersNational Science Foundation
KeywordsMathematicsFibered knot3-manifoldGeneralizationRelatively hyperbolic groupConvexityGroup (periodic table)Pure mathematicsManifold (fluid mechanics)Hyperbolic manifoldSurface (topology)Hyperbolic groupCombinatoricsMapping class groupFundamental groupMathematical analysisGeometryHyperbolic functionPhysics

Abstract

fetched live from OpenAlex

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 .

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Research integrity
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.052
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.000
Bibliometrics0.0010.001
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.002
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.020
GPT teacher head0.264
Teacher spread0.244 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it