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Stability theorems for symplectic and contact pairs

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G. Bande, P. Ghiggini, D. Kotschick

Symplectic Geometry · Submitted 26 Jul 2004

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

The authors' main claim We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs.

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arXiv IDmath/0407442 (version 1)
Pith IDIAXC74C6, Pith's permanent record of this paper and its review
CitationD. Kotschick, G. Bande, P. Ghiggini. "Stability theorems for symplectic and contact pairs." arXiv:math/0407442 (2004). https://pith.science/paper/IAXC74C6
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,345 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.30 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.20 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the condition that its kernel hyperplane distribution have constant class in the sense of E. Cartan.

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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 prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. contribution 0.70 0.95 0.86 asserted 1.00
s1 We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the condition that its kernel hyperplane distribution have constant class in the sense of E. Cartan. contribution 0.99 0.85 0.10 asserted 0.95

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

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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

We prove Gray--Moser stability theorems for complementary pairs of forms of constant class defining symplectic pairs, contact-symplectic pairs and contact pairs. We also consider the case of contact-symplectic and contact-contact structures, in which the constant class condition on a one-form is replaced by the condition that its kernel hyperplane distribution have constant class in the sense of E. Cartan.

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