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Record W3101672505

Homomorphisms between mapping class groups

2016· article· en· W3101672505 on OpenAlex
Javier Aramayona, Juan Souto

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

VenueArrow@dit (Dublin Institute of Technology) · 2016
Typearticle
Languageen
FieldMathematics
TopicGeometric and Algebraic Topology
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsMathematicsGenusHolomorphic functionBoundary (topology)HomomorphismMapping class groupEndomorphismEmbeddingIsomorphism (crystallography)CombinatoricsType (biology)Open mapping theorem (functional analysis)Pure mathematicsSurface (topology)GeometryMathematical analysisBanach spaceEberlein–Šmulian theoremCrystallography
DOInot available

Abstract

fetched live from OpenAlex

Abstract. Suppose that X and Y are surfaces of finite topologi-cal type, where X has genus g ≥ 6 and Y has genus at most 2g−1; in addition, suppose that Y is not closed if it has genus 2g − 1. Our main result asserts that every non-trivial homomorphism Map(X) → Map(Y) is induced by an embedding, i.e. a combina-tion of forgetting punctures, deleting boundary components and subsurface embeddings. In particular, if X has no boundary then every non-trivial endomorphism Map(X) → Map(X) is in fact an isomorphism. As an application of our main theorem we obtain that, under the same hypotheses on genus, if X and Y have finite analytic type then every non-constant holomorphic map M(X) → M(Y) between the corresponding moduli spaces is a forgetful map. In particular, there are no such holomorphic maps unless X and Y have the same genus and Y has at most as many marked points as X. A nuestras madres, cada uno a la suya. 1.

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)0.002
Version: codex-gemma-dda1882f352aValidation 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 score0.152
Threshold uncertainty score0.996

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.002
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0020.002
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0010.000
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 head0.049
GPT teacher head0.277
Teacher spread0.228 · 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