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Record W2900871523 · doi:10.2140/agt.2020.20.3733

Ribbon 2–knots, 1 + 1 = 2 and Duflo’s theoremfor arbitrary Lie algebras

2020· article· en· W2900871523 on OpenAlex
Dror Bar-Natan, Zsuzsanna Dancso, Nancy Scherich

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

VenueAlgebraic & Geometric Topology · 2020
Typearticle
Languageen
FieldMathematics
TopicGeometric and Algebraic Topology
Canadian institutionsUniversity of Toronto
Fundersnot available
KeywordsMathematicsLie algebraPure mathematicsIsomorphism (crystallography)Algebra over a field

Abstract

fetched live from OpenAlex

We explain a direct topological proof for the multiplicativity of the Duflo isomorphism for arbitrary finite-dimensional Lie algebras, and derive the explicit formula for the Duflo map. The proof follows a series of implications, starting with “the calculation [math] on a 4D abacus”, using the study of homomorphic expansions (aka universal finite-type invariants) for ribbon [math] –knots, and the relationship between the corresponding associated graded space of arrow diagrams and universal enveloping algebras. This complements the results of the first author, Le and Thurston, where similar arguments using a “3D abacus” and the Kontsevich integral were used to deduce Duflo’s theorem for metrized Lie algebras; and results of the first two authors on finite-type invariants of w–knotted objects, which also imply a relation of [math] –knots with the Duflo theorem in full generality, though via a lengthier path.

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)0.006
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Insufficient payload (model declined to judge)
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 score0.040
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.006
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.000
Bibliometrics0.0020.005
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0010.001
Insufficient payload (model declined to judge)0.0040.001

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 head0.044
GPT teacher head0.279
Teacher spread0.235 · 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