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The geometry of E-manifolds

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Eva Miranda, Geoffrey Scott

Symplectic Geometry · Submitted 8 Feb 2018

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

The authors' main claim We generalize Moser's theorem to this setting, and use it to construct symplectomorphisms between singular symplectic forms.

how it is stated · asserted 1.00 read the record →

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arXiv ID1802.02959 (version 1)
Pith IDSQONKGSW, Pith's permanent record of this paper and its review
CitationEva Miranda, Geoffrey Scott. "The geometry of E-manifolds." arXiv:1802.02959 (2018). https://pith.science/paper/SQONKGSW
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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, 3,677 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.66 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an $E$-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. This setting generalizes the study of $b$-symplectic manifolds, foliated manifolds, and a wide class of Poisson manifolds. We generalize Moser's theorem to this setting, and use it to construct symplectomorphisms between singular symplectic forms. We give applications of this machinery (including the study of Poisson cohomology), and study specific examples of a few of them in depth.

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 Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an $E$-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. contribution 0.99 0.92 0.11 asserted 0.97
s1 This setting generalizes the study of $b$-symplectic manifolds, foliated manifolds, and a wide class of Poisson manifolds. background 0.48 0.31 0.07 asserted 1.00
s2 We generalize Moser's theorem to this setting, and use it to construct symplectomorphisms between singular symplectic forms. contribution 0.59 0.95 0.34 asserted 1.00
s3 We give applications of this machinery (including the study of Poisson cohomology), and study specific examples of a few of them in depth. contribution 0.99 0.95 0.13 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.65 · evidence from proof or derivation 1.00.

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  • C citations
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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

Motivated by the study of symplectic Lie algebroids, we study a describe a type of algebroid (called an $E$-tangent bundle) which is particularly well-suited to study of singular differential forms and their cohomology. This setting generalizes the study of $b$-symplectic manifolds, foliated manifolds, and a wide class of Poisson manifolds. We generalize Moser's theorem to this setting, and use it to construct symplectomorphisms between singular symplectic forms. We give applications of this machinery (including the study of Poisson cohomology), and study specific examples of a few of them in depth.

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6 arXiv papers cite this in 9 sentences

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Papers citing it · 6 sentences without a confident label

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Cites it as background 1 paper

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