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Record W2067740724 · doi:10.4310/hha.2001.v3.n1.a9

The cohomology ring of free loop spaces

2001· article· en· W2067740724 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.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

VenueHomology Homotopy and Applications · 2001
Typearticle
Languageen
FieldMathematics
TopicHomotopy and Cohomology in Algebraic Topology
Canadian institutionsnot available
FundersNatural Sciences and Engineering Research Council of CanadaUniversity of Toronto
KeywordsMathematicsCohomologyCohomology ringLoop spaceLoop (graph theory)Cup productIsomorphism (crystallography)Pure mathematicsRing (chemistry)Space (punctuation)Dimension (graph theory)Product (mathematics)Commutative ringEquivariant cohomologyCommutative propertyDe Rham cohomologyCombinatoricsGeometryCrystallographyComputer scienceChemistry

Abstract

fetched live from OpenAlex

Let X be a simply connected space and k a commutative ring. Goodwillie, Burghelea and Fiedorowicz proved that the Hochschild cohomology of the singular chains on the space of pointed loops HH * S * (X) is isomorphic to the free loop space cohomology H * (X S 1 ). We prove that this isomorphism is compatible with the usual cup product on H * (X S 1 ) and the cup product of Cartan and Eilenberg on HH * S * (X). In particular, we make explicit the algebra H * (X S 1 ) when X is a suspended space, a complex projective space or a finite CWcomplex of dimension p such that 1 (p-1)! k.

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)0.000
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 score0.053
Threshold uncertainty score0.725

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0010.002
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
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 head0.023
GPT teacher head0.301
Teacher spread0.278 · 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