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I’ve created this discussion following the recent posts in the discussion of fivebrane 6-group and since I have two more points that are unclear to me:
I personally have moved over to writing Fréchet–Lie group (with an en-dash), but I don’t know if this is standard. “Fréchet” as an adjective like in “Fréchet manifold” or “Fréchet space” etc doesn’t have a any type of dash/hyphen.
I guess there’s some kind of unspoken convention around a new type of object whose name is “from a person” when it already has such a name. I don’t know if it’s consistent. There are things like Grothendieck–Riemann–Roch, which doesn’t seem like it is ever “Grothendieck Riemann-Roch” (but people do say “Grothendieck’s Riemann-Roch theorem”, but that clearly doesn’t work for objects like infinite-dimensional Lie groups).
This to some extent highlights the known issues with using people’s names to name types of objects, that’s not a nLab problem, and a much harder discussion to resolve.
On a gut level I find that “Spin group” is more pleasant to the eye than “spin group”. But nLab convention is that only names be capitalized, usually understood as: names of people and titles of texts, not names of mathematical concepts. Therefore it should probably be lower case, and with it “fivebrane group” etc.
On the hyphens I have no opinion. But the two instances you quote make some sense in themselves, in that Conner & Floyd were coauthors of each other, but not of Chern.
On the superscipts: While I was the one who created the entries titled “spin^c” and “MSpin^c”, I never liked their look, just didn’t know what else to do. Your fix using unicode seems clearly superior. I will take the liberty of implementing that for these entries right now.
Concerning Conner-Floyd Chern class: If that decides about hyphens, what about articles like Einstein-Yang-Mills-Dirac-Higgs theory?
I’m planning to create articles for “Banach Lie group/Banach-Lie group” and “Hilbert Lie group/Hilbert-Lie group”. Which title should I use?
I won’t claim that it “decides” it, just observed that it “makes some sense”.
Just on a case-by-case basis:
I feel that “Chern class” is a stand-alone term. Hence if X, Y & Z come and define a variant Chern class it derserves to be called “X-Y-Z Chern class” instead of X-Y-Z-Chern class.
This seems different for “Einstein-Yang-Mills-Dirac-Higgs theory”. If anything, then the pair Yang & Mills here is special, since these are like Conner & Floyd above in that their contribution is through a joint authorship. So on pure logic it would make sense to write “Einstein Yang-Mills Dirac Higgs theory”, if it were not for the fact that this seems to have too many whitespaces to be pleasantly readable.
In conclusion, I doubt we can find a general rule here that is always applicable. We need to see on a case-by-case basis what works well.
Regarding Banach Lie groups and Hilbert Lie group, I might tend to write them without hyphen.
BUT in any case, none of this should delay you in creating an entry! Just create it with any name and b sure to add all reasonable redirects, then no harm will be caused.
No problem, “Banach Lie group” and “Hilbert Lie group” it is (or will be).
If that’s the case, then to close a question in the original post, it will also be Fréchet Lie group, no hyphen.
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