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Record W2964232475 · doi:10.4310/mrl.2008.v15.n1.a6

The $K$-theory of abelian symplectic quotients

2008· article· en· W2964232475 on OpenAlexafffund
Megumi Harada, Gregory D. Landweber

Bibliographic record

VenueMathematical Research Letters · 2008
Typearticle
Languageen
FieldMathematics
TopicAdvanced Combinatorial Mathematics
Canadian institutionsMcMaster University
FundersBanff International Research Station for Mathematical Innovation and DiscoveryUniversity of TorontoAmerican Institute of Mathematics
KeywordsMathematicsSymplectic geometryMoment mapEquivariant mapMorse theoryPure mathematicsMaximal torusQuotientSymplectic manifoldEquivariant cohomologyAlgebra over a fieldDiscrete mathematicsCohomologyLie algebra

Abstract

fetched live from OpenAlex

Let T be a compact torus and (M, ) a Hamiltonian T -space. In a previous paper, the authors showed that the T -equivariant K-theory of the manifold M surjects onto the ordinary integral K-theory of the symplectic quotient M//T , under certain technical conditions on the moment map. In this paper, we use equivariant Morse theory to give a method for computing the K-theory of M//T by obtaining an explicit description of the kernel of the surjection : K * T (M ) K * (M//T ). Our results are K-theoretic analogues of the work of Tolman and Weitsman for Borel equivariant cohomology. Further, we prove that under suitable technical conditions on the T -orbit stratification of M , there is an explicit Goresky-Kottwitz-MacPherson ("GKM") type combinatorial description of the K-theory of a Hamiltonian T -space in terms of fixed point data. Finally, we illustrate our methods by computing the ordinary K-theory of compact symplectic toric manifolds, which arise as symplectic quotients of an affine space C N by a linear torus action.

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 machine prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.001
Version: metacan-v3-hybrid-931329e0061cValidation 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 score0.003
Threshold uncertainty score0.010

Distilled classifier scores by category (both heads)

CategoryCodexGemma
Metaresearch0.0000.001
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0020.001
Science and technology studies0.0010.003
Scholarly communication0.0020.003
Open science0.0010.002
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0030.000

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 head0.185
GPT teacher head0.414
Teacher spread0.229 · 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 source (direct Gemma or distilled Codex), not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
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

Citations18
Published2008
Admission routes2
Has abstractyes

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