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Record W2010241938 · doi:10.1112/jtopol/jtt042

The topological period-index problem over 6-complexes

2013· article· en· W2010241938 on OpenAlexaff
Benjamin Antieau, Ben Williams

Bibliographic record

VenueJournal of Topology · 2013
Typearticle
Languageen
FieldMathematics
TopicAlgebraic Geometry and Number Theory
Canadian institutionsUniversity of British Columbia
Fundersnot available
KeywordsMathematicsSurjective functionPure mathematicsPeriod (music)CohomologyConjectureUnitary stateSheafTopology (electrical circuits)Combinatorics

Abstract

fetched live from OpenAlex

By comparing the Postnikov towers of the classifying spaces of projective unitary groups and the differentials in a twisted Atiyah–Hirzebruch spectral sequence, we deduce a lower bound on the topological index in terms of the period, and solve the topological version of the period–index problem in full for finite CW complexes of dimension less than 6. Conditions are established that, if they were met in the cohomology of a smooth complex 3-fold variety, would disprove the ordinary period–index conjecture. Examples of higher-dimensional varieties meeting these conditions are provided. We use our results to furnish an obstruction to realizing a period-2 Brauer class as the class associated to a sheaf of Clifford algebras, and varieties are constructed for which the total Clifford invariant map is not surjective. No such examples were previously known.

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 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 categoriesInsufficient 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 score0.043
Threshold uncertainty score0.997

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0040.000

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 head0.024
GPT teacher head0.300
Teacher spread0.276 · 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 teacher head, not a consensus.

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

Citations42
Published2013
Admission routes1
Has abstractyes

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