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Record W2089124265 · doi:10.1007/s00039-009-0706-y

The Arnoux–Yoccoz Teichmüller disc

2009· article· en· W2089124265 on OpenAlexaff
Pascal Hubert, Erwan Lanneau, Martin Möller

Bibliographic record

VenueGeometric and Functional Analysis · 2009
Typearticle
Languageen
FieldMathematics
TopicMathematical Dynamics and Fractals
Canadian institutionsCegep de Saint Jerome
FundersAgence Nationale de la Recherche
KeywordsMathematicsDiffeomorphismQuadratic differentialPure mathematicsHolomorphic functionTotally geodesicGeodesicLocus (genetics)GenusQuadratic equationSurface (topology)CombinatoricsMathematical analysisGeometry

Abstract

fetched live from OpenAlex

We prove that the Teichmüller disc stabilized by the Arnoux-Yoccoz pseudo-Anosov diffeomorphism contains at least two closed Teichmüller geodesics. This proves that the corresponding flat surface does not have a cyclic Veech group.In addition, we prove that this Teichmüller disc is dense inside the hyperelliptic locus of the connected component $${\mathcal{H}}^{\rm odd}$$ (2,2) . The proof uses Ratner’s theorems.Rephrasing our results in terms of quadratic differentials, we show that there exists a holomorphic quadratic differential, on a genus 2 surface, with the two following properties: 1. The Teichmüller disc is dense inside the moduli space of holomorphic quadratic differentials (which are not the global square of any Abelian differentials). 2. The stabilizer of the $${\rm PSL}_2$$ ( $${\mathbb{R}}$$ )-action contains two non-commuting pseudo-Anosov diffeomorphisms.

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.

How this classification was reachedexpand

Full frame machine prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: metacan-v3-hybrid-931329e0061cValidation status: machine_predicted_unvalidated
Candidate categoriesnone
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 score0.002
Threshold uncertainty score0.008

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.000
Science and technology studies0.0010.001
Scholarly communication0.0010.001
Open science0.0000.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0020.000

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 head0.025
GPT teacher head0.269
Teacher spread0.243 · 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

Classification

machine, unvalidated

Machine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations15
Published2009
Admission routes1
Has abstractyes

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