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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeSep 10th 2018
• (edited Sep 10th 2018)

table highlighting the pattern in the “Segal completion theorems”: Atiyah-Segal completion theorem and Segal-Carlsson completion theorem. Not a stand-alone entry, but for !inclusion into the various entries that the table relates to

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeSep 11th 2018

added another row to the table for the Rector completion theorem

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeSep 12th 2018

This table is one example of many nLab pages that are rendered properly only with Firefox.

Since I am receiving emails about problems, I am wondering if it might be worthwhile to add a general remark to all nLab pages. Something like “best viewed with Firefox”, or the like.

• CommentRowNumber4.
• CommentAuthorRichard Williamson
• CommentTimeSep 12th 2018
• (edited Sep 12th 2018)

Yes, MathJax cannot seem to parse links within mathematics, it is only browsers that are rendering the MathML directly that seem to be able to do so. I have seen the problem most often in tables. I am not aware of any other significant cases, I think.

This is very unfortunate, but I personally would be reluctant to add such a remark to all pages. I for example never use Firefox (except occasionally when testing) , and have no problems for almost all pages I look at. Also on a mobile, for instance, one does not have the possibility to use Firefox.

I would suggest to instead flag the particular cases where there is an issue (links within mathematics, for instance) on the Technical TODO list (nlabmeta). I have been working on a new TeX renderer which is neither MathJax nor itex2MML, and this kind of thing could be one place where I could try to introduce it, maybe in such a way that the MathML is still used on Firefox.

Please feel free to forward relevant sections of emails to me, either over email itself or here on the nForum.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeSep 12th 2018

Also on a mobile, for instance, one does not have the possibility to use Firefox.

Interesting that you say that. I use Firefox on my phone all the time. Because with Chrome on my phone, all the math formulas on the nLab come out tiny and with lacking whitespace.

• CommentRowNumber6.
• CommentAuthorRichard Williamson
• CommentTimeSep 12th 2018
• (edited Sep 12th 2018)

Ah, apologies, that was nonsense. I believe it is very little used relative to other mobile browsers, though. You are correct about the formulas, I would regard this as a ’bug’ in MathJax, although it is hard to fix; I have encountered the same in my experiments with a new renderer: one wishes to use ’inline-block’ in the CSS to prevent the mathematics from being split at line breaks, but this seems to cause the behaviour you describe in some cases, especially on a mobile. So I am just allowing line breaks at the moment. See for example foundation of mathematics, where I have used my new renderer: the mathematics (e.g. the inline diagram after the words ’specific product cone’) displays fine for me in Chrome on a mobile, but looks like you describe if MathJax is used.

• CommentRowNumber7.
• CommentAuthorAlizter
• CommentTimeSep 13th 2018
The formulae say "unknown node type" and are not rednering properly.
• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeSep 13th 2018
• (edited Sep 13th 2018)

Yeah, that’s for non-Firefox browsers. Elsewhere I was suggesting to add a general alert to pages, that only Firefox renders the nLab properly.

• CommentRowNumber9.
• CommentAuthorDavid_Corfield
• CommentTimeOct 5th 2018

I see from Equivariant stable homotopy theory that there’s a larger story here. First, that some of these completions for cohomology are accompanied by localizations for homology, e.g., for K-theory but not for cohomotopy. Second, that the completion/localization account works more broadly to include complex cobordism and modules over $M U$.

I guess we could expand the table at least with the latter. What’s the equivariant complex cobordism ring of the point?

[I was drawn here by a wish to reference someone using induced and coinduced actions for group homomorphisms.]

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeOct 24th 2018

added a first line for equivariant ordinary cohomology – for completeness (…pun intended)

• CommentRowNumber11.
• CommentAuthorDavid_Corfield
• CommentTimeOct 26th 2018

As mentioned in #9, a similar completion has been found for MU (and its modules). So I added it to the table.

• CommentRowNumber12.
• CommentAuthorUrs
• CommentTimeOct 26th 2018

Thanks, I seem to have missed #9 when you wrote it, and still when I wrote #10.

But so we should add some pointer/citation with your new row in the table.

• CommentRowNumber13.
• CommentAuthorDavid_Corfield
• CommentTimeOct 26th 2018

I don’t know if it has a name. Greenlees and May in Localization and Completion Theorems for MU-Module Spectra say Löffler sketched a proof and Comezana and May completed it.

• CommentRowNumber14.
• CommentAuthorUrs
• CommentTimeOct 26th 2018

would be good to find the reference, add the statement on the nLab, and then link to there from that table…