Talk:WikiJournal User Group/Poisson manifold

Plagiarism check
✅ Report from WMF copyvios tool only showed overlap in book titles in the reference section.  OhanaUnited  Talk page  19:42, 24 June 2023 (UTC)

First peer review
 OhanaUnited  Talk page  21:10, 11 September 2023 (UTC)


 * I thank the reviewer for the thorough and useful comments. I have implemented all of his corrections and suggestions (with one exception - see below); in particular (I will not mention fixing typos in the text or the formulas),
 * - I fixed the convention of the Poisson bracket of a symplectic form
 * - I rewrote the ambiguous sentences in the 5th and 6th paragraph of the introduction as suggested
 * - in "Equivalence of the definition" I rephrased the definition of almost Poisson structure as suggested
 * - in "Symplectic leaves" I changed singular foliation into singular distribution
 * - in "Rank of a Poisson structure" I added the word open and removed the reference to M_reg = M
 * - in "Nondegenerate Poisson structures" I added the connectedness hypothesis and I removed the reference to Poisson rings (I realised it is not a commonly used algebraic notion; actually, I could not find it in any source besides the wikipedia page Poisson ring, which has indeed no reference)
 * - in "Fibrewise linear Poisson structures" I fixed the claim on the symplectic leaves of A^* and added the suggested remark
 * - in "Other examples and constructions" I replaced "by Poisson diffeomorphisms" with the suggested condition
 * - in "Modular class" I added the orientability hypothesis and then explained that it can be removed by replacing volume forms with densities, adding a reference
 * - in "Poisson maps" I added the word "forward" to Dirac map, adding a reference; I also added a line involving general Poisson/symplectic maps between symplectic manifolds, as suggested
 * - in "Symplectic realisation" I rewrote the sentence which contained "this last condition"
 * - in "Integration of Poisson manifolds" I added the appropriate references
 * - in "Symplectic groupoid" I added the hypothesis of s-simply connectedness when needed and fixed/updated the references
 * - in "Examples of integrations" I replaced "the" with "a" and removed the request of simply connectedness for G
 * - in "Submanifolds" I rewrote the definition of Poisson submanifold
 * The only exception involves the comment on the opening sentence. While I completely agree with the reviewer that something of the kind "A Poisson manifold is a smooth manifold endowed with a Poisson structure. The notion of Poisson manifold generalises..." would be the most appropriate opening for a paper in a mathematics journal, I believe that the Wikijournal of Science prefers a less mathematical-heavy introduction.
 * Indeed, my first sentence is the standard opening for the majority of wikipedia articles involving topics in advance mathematics (compare e.g. with Symplectic manifold or other manifolds with an extra structure): "In X, a field of mathematics, a Y is a Z blablabla", where Z is a more basic notion than Y, which however does not prevent the non-expert reader to finish to read the sentence (and, ideally, the wikilinks would point to the readers what they should be familiars in order to read further).
 * I realise however that the difference might be very minor, therefore I would like to ask the editors' opinion: I am open to any reasonable change on this matter.
 * PS for the editors: I have also implemented a few minor corrections (basically only typos) to reflect the new edits made in the last months by other users (or citation bots) on the original wikipedia page on which this article is adapted. Francesco Cattafi (discuss • contribs) 17:45, 22 October 2023 (UTC)

Style of the references
I have a further question for the editors (I realised this issue only while implementing some of the reviewer's comments). In the original wikipedia articles I added several wikilinks into each item in the bibliography (basically linking the pages of the authors and of the journals, when available): all such links have been lost when transporting the article from wikipedia to wikiversity.

Similarly, in the articles written in French, the English translation of the title disappeared; last, most of the references had also a link to the Arxiv (pointing to the open access version of those papers), which was removed as well.

I was wondering if this has been intentional, i.e. it is the journal policy to minimize the data of each reference item, or if the missing parts/links have been simply a collateral damage during the transportation of the article, and, therefore, I can/should restore them. Francesco Cattafi (discuss • contribs) 17:58, 22 October 2023 (UTC)


 * I don't know. What does the edit history tell you? Physikerwelt (discuss • contribs) 07:49, 18 June 2024 (UTC)
 * @Francesco Cattafi and @Physikerwelt, I have narrowed it down to a a series of edits in March 2023 which removed "|author-link=" to the respective references. These edits took out the wikilinks to the authors and journal names. In my opinion, it's non-standard to link to the Wikipedia page of specific authors or journals. Not sure about the French articles. Can you point to which reference that is in French? As far as I can tell, Arxiv is still embedded in cite journal. However, I think the template supersedes the Arxiv field if URL field is filled.  OhanaUnited  Talk page  19:31, 18 June 2024 (UTC)
 * @OhanaUnited thank you for investing. This explains what happened.
 * @Evolution and evolvability what was the rational to remove links and author references? Physikerwelt (discuss • contribs) 06:40, 19 June 2024 (UTC)


 * Thank you all for the replies. Regarding the author and journal links, I was following the Cite Journal template, which has indeed an author-link parameter (so I assumed it should be used, when possible) and states, regarding the journal, "may be wikilinked".
 * You are right regarding the Arxiv links, it seems that it is simply not displayed in wikiversity, as opposed to wikipedia. The articles in French are those referenced as 1, 4, 13, 16 and 28. Francesco Cattafi (discuss • contribs) 19:37, 26 June 2024 (UTC)

Second Review

 * I thank the reviewer for the thorough and useful comments; I have implemented all of his suggestions.


 * 1) I have reduced the section on symplectic realisations and moved it the end of the section on integration of Poisson manifolds. In particular, I have removed the technical discussions on the adjective "full" and the three examples (which were indeed redundant, since they are the same examples already discussed in the integration of Poisson manifolds). Now only a couple of paragraphs are left, simply explaining the relations between (complete) symplectic realisations and integrability.


 * 2) I renamed the Weinstein groupoid as Severa-Weinstein groupoid and added the appropriate reference. Notice however that this article has a link to the wikipedia page Lie algebroid, where such object is discussed still under the name Weinstein groupoid - I will soon update that page as well with the more complete name and reference. Edit: I have added the name Severa-Weinstein groupoid also in that page, updating the wikilink.


 * 3) I removed the unconvincing motivation which linked Poisson submanifolds to Poisson transversal and improved the exposition on submanifolds. Now there is a section on Poisson submanifolds, followed by a list of examples, and then a section on "other submanifolds in Poisson geometry", which contains the previous paragraph on Poisson transversals, as well as a new paragraph on coisotropic submanifolds.


 * 4) I have added in the section "Linear Poisson structures" the explicit expression in coordinates for two simple Lie-Poisson structures, namely those of so(3,R)^* and sl(2,R)^*. Moreover, I added another simple example in coordinates of a log-symplectic structures (another important class of Poisson manifolds which was not mentioned elsewhere in the article).


 * 5) I have added a section "Further topics" covering deformation quantisation, the linearisation problem and Poisson-Lie groups. Notice that I have added a "see also" template linking to the existing wikipedia page on Poisson-Lie groups, where they are treated in more details (unlike the other two topics, which currently do not have a separate page - even if they probably would deserve one).


 * Francesco Cattafi (discuss • contribs) 19:32, 26 June 2024 (UTC)