The $K$-theory of abelian symplectic quotients
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Bibliographic record
Abstract
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.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.028 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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 it