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On Fixed Points of a Map Defined by Alain Connes

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Hongbo Zhao

Quantum Algebra · Submitted 21 Nov 2019

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

The authors' main claim It turns out that the the non-zero fixed points of the map can be characterized explicitly as an abelian group, and we can calculate some examples.

how it is stated · asserted 1.00 read the record →

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arXiv ID1911.09463 (version 1)
Pith ID2BD6GUPD, Pith's permanent record of this paper and its review
CitationHongbo Zhao. "On Fixed Points of a Map Defined by Alain Connes." arXiv:1911.09463 (2019). https://pith.science/paper/2BD6GUPD
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,936 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.90 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.10 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In this paper we study certain analogues of the map defined by Alain Connes, which follows an idea of Atiyah in trying to simplify the proof of Feit-Thompson theorem. It turns out that the the non-zero fixed points of the map can be characterized explicitly as an abelian group, and we can calculate some examples. It turns out that most fixed points are not one dimensional representations for these examples, and much work need to be done.

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 In this paper we study certain analogues of the map defined by Alain Connes, which follows an idea of Atiyah in trying to simplify the proof of Feit-Thompson theorem. background 0.65 0.36 0.04 asserted 0.96
s1 It turns out that the the non-zero fixed points of the map can be characterized explicitly as an abelian group, and we can calculate some examples. result 0.99 0.92 0.68 asserted 1.00
s2 It turns out that most fixed points are not one dimensional representations for these examples, and much work need to be done. result 0.42 0.85 0.13 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.99.

What was examined, and what was not

sources read
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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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

In this paper we study certain analogues of the map defined by Alain Connes, which follows an idea of Atiyah in trying to simplify the proof of Feit-Thompson theorem. It turns out that the the non-zero fixed points of the map can be characterized explicitly as an abelian group, and we can calculate some examples. It turns out that most fixed points are not one dimensional representations for these examples, and much work need to be done.

Human review

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 6 sentences without a confident label

Compares with 1 paper
  • This is exactly Proposition 2.1 in [ref] which was proved in a different way.

    On an idea of Michael Atiyah · Analytic Properties of $Ψ_t$ · 0.93

Cites as background 1 paper
  • To define the maps we give a brief overview of the main idea of the paper [ref] by Connes, and recall some `natural operations' such as $λ$-operations and Adams operations.

    On an idea of Michael Atiyah · The Maps $Λ_t$ and $Ψ_t$ · 0.92

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