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On complexes related with calculus of variations

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Hovhannes Khudaverdian, Theodore Voronov

Differential Geometry · Submitted 27 May 2001

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

The authors' main claim We establish relation of the complex of variational derivatives and the variational complex.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0105223 (version 1)
Pith IDVAVVQFQ4, Pith's permanent record of this paper and its review
CitationHovhannes Khudaverdian, Theodore Voronov. "On complexes related with calculus of variations." arXiv:math/0105223 (2001). https://pith.science/paper/VAVVQFQ4
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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, 4,765 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.04 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.08 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The discussion of the variational (bi)complex is set up in terms of a flat connection in the jet bundle. We extend it to supercase using a particular new class of forms. We establish relation of the complex of variational derivatives and the variational complex. Certain calculus of Lagrangians of multidimensional paths is developed. It is shown how covariant Lagrangians of higher order can be used to represent characteristic classes.

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 variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. contribution 0.96 0.87 0.13 asserted 0.90
s1 The discussion of the variational (bi)complex is set up in terms of a flat connection in the jet bundle. method 0.95 0.62 0.05 asserted 1.00
s2 We extend it to supercase using a particular new class of forms. contribution 0.88 0.92 0.07 asserted 1.00
s3 We establish relation of the complex of variational derivatives and the variational complex. result 0.75 0.91 0.45 asserted 1.00
s4 Certain calculus of Lagrangians of multidimensional paths is developed. contribution 0.98 0.82 0.09 asserted 0.98
s5 It is shown how covariant Lagrangians of higher order can be used to represent characteristic classes. result 0.92 0.84 0.23 asserted 1.00

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

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  • references and citing sentences
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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

We consider the variational complex on infinite jet space and the complex of variational derivatives for Lagrangians of multidimensional paths and study relations between them. The discussion of the variational (bi)complex is set up in terms of a flat connection in the jet bundle. We extend it to supercase using a particular new class of forms. We establish relation of the complex of variational derivatives and the variational complex. Certain calculus of Lagrangians of multidimensional paths is developed. It is shown how covariant Lagrangians of higher order can be used to represent characteristic classes.

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4 arXiv papers cite this in 4 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

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