440:, Princeton University Press: 1950) disappointingly seem to propagate the misconception that associated bundles are some kind of mysterious concept. Now I may have missed some particular subtlety, but my understanding is that (using Steenrod's nomenclature) two bundles are associated if and only if they are associates of the same principal bundle. So I find the very idea of "associated bundles" to be a bit of a non sequitur. I don't mean to say that the article shouldn't exist, but I do believe that it can be clarified extensively. I moved a few of the vague sections into the talk page for now.
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510:′. I find this definition to be a bit disingenuous because it already slips the principal bundle in through the back door. But you're basically right. I can see how this definition through "subterfuge" can be more easily understood by someone who isn't yet comfortable with principal bundles. I'll do my best to preserve the spirit, if not the actual letter, of the article. Thanks for sorting me out,
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I, for one, find the principal bundle picture more intuitive. (Of course, I've been working with them for some time, so I am indeed already biased.) Perhaps we should compromise. The idea behind associated bundles is just that they have the same structure group and "the same" transition functions
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I admit that I'm not all that familiar with the most general definition of an associated bundle. But in common parlance among my circles, an associated bundle is simply a bundle associated to a principal bundle by means of a
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Is this article only for people who already know how to guess the meaning of obscure and seemingly extremely context-dependent jargon such as these two never-defined-in-this-article labels?
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data for transition on intersections; and then make the obseveration that the same G-valued data gives you many associated bundles. I suppose this page was awaiting proper definition of
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There is a small issue here (you may be right about squeamishness about principal bundles, actually). It's just that for a faithful action of group
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This article does not actually define what the associated bundle construction is.
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When I get the chance, I intend to export reduction of the structure group to
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construction, in a different light. This does suggest there will be some
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Can't we just say what it is without all of the subterfuge?
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Export reduction of structure group to
Principal Bundles
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