Talk:Bundle (mathematics)

Meaning of bundle
Is it? Charles Matthews 21:04, 15 Jul 2004 (UTC)

"In mathematics, a bundle is nothing more or less than an element of an infinite product."
 * Huh??? Do you mean the space of sections of a bundle? But even then, that ignores the topology. Phys 18:58, 6 Aug 2004 (UTC)

"The category of bundles over B is therefore just the comma category (C↓B) of objects over B..."
 * Why would an arbitrary morphism in the comma category necessarily be an epimorphism?

What to do with this?
I was rather surprised to find this when I searched for "bundle"! The first paragraph seems to be more like the definition of a fibration than a bundle, although the fibration article itself is more restrictive, requiring the homotopy lifting property. However, without any other conditions, a fibre bundle without local triviality (local product structure) is nothing more than a (possibly surjective) continuous map. Is there any reference for using the term "bundle" for an arbitrary surjection?

The rest of the article would seem to be on Bundle_(category theory), and probably doesn't all belong under a general title like this, although the idea of the category of bundles being a bundle is nice. Again, though, it would be nice to know that category theorists actually do use the term "bundle" for epimorphisms in a comma category - is there a reference?

For a differential geometer like me, "bundle" either means "smooth fiber bundle", or something slightly weaker, like "surjective submersion". I think that for many mathematicians, "bundle" and "fiber bundle" are synonymous. A general article ought to reflect the common (but varied) usages.

My initial feeling is that this could become an article about the general notion of parameterized families of objects (the fibres are parameterized by points in the base), with links to other articles for particular cases. This is an important notion which arises in homotopy theory, differential geometry, algebraic geometry (e.g. schemes, moduli spaces, tautological and universal families), etc. Still, I'm not completely convinced that "bundle" is the right word for the general notion. What do others think? Geometry guy 16:45, 10 February 2007 (UTC)


 * I believe Husemoller in his book Fibre Bundles, defines a bundle this way (not even requiring surjectivity). If I recall, he claims in the preface that the idea is due to Grothendieck. I have no idea how wide spread this usage is. In my experience "bundle" is synonymous with "fiber bundle". -- Fropuff 17:21, 10 February 2007 (UTC)


 * The idea of a morphism as a parameterized family of objects is almost certainly due to Grothendieck, and the ramifications in algebraic geometry have been quite profound. However, Grothendieck wrote in French, and I doubt he used any term similar to "bundle". Anyway, I'm glad you share my perception that "bundle" usually means "fiber bundle". Geometry guy 02:01, 11 February 2007 (UTC)

Meaning of bundle 2
Is it possible to describe a bundle of the mathematical sort in even some difficult terms a layman could still possibly make some sense of, in a small section at the bottom I mean? Aren't there any shapes or forms in these spaces beneath the thoroughly abstract definition? The vast majority of mathematics articles on Wikipedia seem to scoff at any suggestions like this. I'm considering how the good ol Brittanica tried to not be so damn terse and purely formal. Is that what Wikipedia is for? Oh sure, go read that old dino if I don't like it you say. —Preceding unsigned comment added by 71.15.148.130 (talk) 11:42, 30 January 2010 (UTC)

Definition
I organized the material a little bit and added a formal definition together with definition of basic terminology. The reference is Husemoller. YohanN7 (talk) 09:43, 7 July 2014 (UTC)