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Torus actions on compact quotients

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Anton Deitmar

dg-ga · Submitted 30 Apr 1996

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action of H on the (infinite dimensional) tangential cohomology.

how it is stated · asserted 1.00 read the record →

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arXiv IDdg-ga/9604008 (version 3)
Pith IDZXJWMQ53, Pith's permanent record of this paper and its review
CitationAnton Deitmar. "Torus actions on compact quotients." arXiv:dg-ga/9604008 (1996). https://pith.science/paper/ZXJWMQ53
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,941 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.13 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We consider the action of a noncompact torus H on the compact quotient G/L, where G is a Lie group containing H and L is a uniform lattice in G. Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action of H on the (infinite dimensional) tangential cohomology. The formula may be viewed as a Lefschetz formula or an equivariant index theorem for noncompact group actions.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We consider the action of a noncompact torus H on the compact quotient G/L, where G is a Lie group containing H and L is a uniform lattice in G. background 0.64 0.54 0.04 asserted 0.83
s1 Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action of H on the (infinite dimensional) tangential cohomology. result 0.55 0.96 0.74 asserted 1.00
s2 The formula may be viewed as a Lefschetz formula or an equivariant index theorem for noncompact group actions. interpretation 1.00 0.57 0.34 hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We consider the action of a noncompact torus H on the compact quotient G/L, where G is a Lie group containing H and L is a uniform lattice in G. Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action of H on the (infinite dimensional) tangential cohomology. The formula may be viewed as a Lefschetz formula or an equivariant index theorem for noncompact group actions.

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