Bibliographic record
Abstract
In this paper we present the construction of explicit quasi-isomorphisms that compute the cyclic homology and periodic cyclic homology of crossed-product algebras associated with (discrete) group actions.In the first part we deal with algebraic crossed-products associated with group actions on unital algebras over any ring k Ą Q.In the second part, we extend the results to actions on locally convex algebras.We then deal with crossed-products associated with group actions on manifolds and smooth varieties.For the finite order components, the results are expressed in terms of what we call "mixed equivariant cohomology".This "mixed" theory mediates between group homology and de Rham cohomology.It is naturally related to equivariant cohomology, and so we obtain explicit constructions of cyclic cycles out of equivariant characteristic classes.For the infinite order components, we simplify and correct the misidentification of [20].An important new homological tool is the notion of "triangular S-module".This is a natural generalization of the cylindrical complexes of Getzler-Jones.It combines the mixed complexes of Burghelea-Kassel and parachain complexes of Getzler-Jones with the S-modules of Kassel-Jones.There are spectral sequences naturally associated with triangular S-modules.In particular, this allows us to recover spectral sequences of Feigin-Tsygan and Getzler-Jones and leads us to a new spectral sequence.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot 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.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.011 | 0.001 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".