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Superconnections and Index Theory

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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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Alexander Kahle

Differential Geometry · Submitted 5 Oct 2008

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

The authors' main claim In particular, we prove a local index theorem for such operators, and for families of such operators.

how it is stated · asserted 1.00 read the record →

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arXiv ID0810.0820 (version 2)
Pith IDAVNZTOPY, Pith's permanent record of this paper and its review
CitationAlexander Kahle. "Superconnections and Index Theory." arXiv:0810.0820 (2008). https://pith.science/paper/AVNZTOPY
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,894 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate eta-invariants and prove an APS-theorem, and construct a geometric determinant line bundle for families of such operators, computing its curvature and holonomy in terms of familiar index theoretic quantities.

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 investigate index theory in the context of Dirac operators coupled to superconnections. contribution 0.88 0.85 0.07 asserted 0.83
s1 In particular, we prove a local index theorem for such operators, and for families of such operators. result 0.65 0.95 0.39 asserted 1.00
s2 We investigate eta-invariants and prove an APS-theorem, and construct a geometric determinant line bundle for families of such operators, computing its curvature and holonomy in terms of familiar index theoretic quantities. contribution 0.78 0.95 0.36 asserted 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

sources read
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not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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 investigate index theory in the context of Dirac operators coupled to superconnections. In particular, we prove a local index theorem for such operators, and for families of such operators. We investigate eta-invariants and prove an APS-theorem, and construct a geometric determinant line bundle for families of such operators, computing its curvature and holonomy in terms of familiar index theoretic quantities.

Human review

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References
How the literature uses it

2 arXiv papers cite this in 8 sentences

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

Papers citing it · 5 sentences without a confident label

Uses its method or tool 1 paper
Cites it as background 1 paper
  • We will not try to make the statements mathematically rigorous.[See, e.g., [ref] for mathematically rigorous description of index theorems using the superconnection.] Nevertheless, we hope they are useful and worth mentioning.

    Anomaly and Superconnection · Index theorems · 0.93

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