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Record W2172168984 · doi:10.24033/asens.2165

The signature package on Witt spaces

2012· preprint· fr· W2172168984 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

VenueAnnales Scientifiques de l École Normale Supérieure · 2012
Typepreprint
Languagefr
FieldMathematics
TopicAdvanced Operator Algebra Research
Canadian institutionsnot available
FundersCentre National de la Recherche ScientifiqueSapienza Università di RomaCentre de Recherches MathématiquesÉcole Normale SupérieureNational Science Foundation
KeywordsParametrixSignature (topology)MathematicsOperator (biology)Pure mathematicsInjective functionDiscrete mathematicsDifferential operatorSemi-elliptic operatorGeometry

Abstract

fetched live from OpenAlex

A. -In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold X which satisfies the Witt condition. This construction, which is inductive over the 'depth' of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index-the analytic signature of X--is well-defined. This provides an alternate approach to some well-known results due to Cheeger. We then prove some new results. By coupling this parametrix construction to a C * r Mishchenko bundle associated to any Galois covering of X with covering group , we prove analogues of the same analytic results, from which it follows that one may define an analytic signature index class as an element of the K-theory of C * r . We go on to establish in this setting and for this class the full range of conclusions which sometimes goes by the name of the signature package. In particular, we prove a new and purely topological theorem, asserting the stratified homotopy invariance of the higher signatures of X, defined through the homology L-class of X, whenever the rational assembly map

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)0.005
metaresearch head score (Gemma)0.002
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies, Scholarly communication, Research integrity, Insufficient payload (model declined to judge)
Consensus categoriesMeta-epidemiology (narrow), Research integrity, Insufficient payload (model declined to judge)
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.460
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0050.002
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0010.001
Bibliometrics0.0000.001
Science and technology studies0.0030.002
Scholarly communication0.0020.001
Open science0.0030.002
Research integrity0.0010.005
Insufficient payload (model declined to judge)0.0010.002

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 head0.050
GPT teacher head0.335
Teacher spread0.286 · 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