Talk:Stiefel–Whitney class

Notes & Queries

Jon Awbrey 06:54, 5 February 2006 (UTC)[reply]

The main section needs touching up. The math displays are not in line with the text.

Postnikov Towers

Would you know if the sw classes can be defined through Postnikov towers etc? —Preceding unsigned comment added by 155.198.157.118 (talk) 19:24, 18 February 2008 (UTC)[reply]

Care to clarify? They already are defined in terms of Postnikov towers. They're pull-backs of maps to Eilenberg-Maclane spaces which have the simplest Postnikov system you can hope for. Rybu (talk) 18:42, 18 August 2008 (UTC)[reply]

More Information

Not enough explanation is given in this article. This is a complex concept, but it shouldn't be inaccessable. This is shown by Milnor's "Characteristic Classes". For example, in the very first axiom you use the notation $f^{*}$ where $w(f^{*}E)=f^{*}w(E)$ . Now what does $f^{*}$ mean in this context? Is it the induced bundle, is the pull back? Any one that didn't already know wouldn't be able to learn it from here, and what's the point of writing an article for people that already know what you're saying? Dharma6662000 (talk) 17:17, 18 August 2008 (UTC)[reply]

In defense of the article, you're asking for the Stiefel-Whitney class article to give definitions of the main constructions in cohomology and vector bundles. An interested reader can pull up the vector bundle or cohomology article and get the appropriate definitions. Moreover, it's appropriate to keep some amount of compartimentalisation otherwise you create articles full of so many peripheral (ie: beside-the-point) details that the main point is lost. We're not here to rewrite Milnor and Stasheff. Rybu (talk) 18:39, 18 August 2008 (UTC)[reply]

I agree, but the article doesn't even say what

f^{*}

is. How can you look it up if you don't know what it is. A simple line saying "...where

f*E

denotes the induced bundle." would make things better. I'm not asking anyone to rewite Milnor and Stasheff, I'm just asking for what is written to be clear. These articles take a long time to write, and so you would hope that they are read and made use of. Becoming defensive over constructive critisism isn't the way to help this article improve. Dharma6662000 (talk) 18:42, 18 August 2008 (UTC)[reply]

Right, the only way to improve the article is to work on it. Rybu (talk) 19:31, 18 August 2008 (UTC)[reply]

Is it really necessary to explain definitions of stuff like Z/2Z or line bundles in the article? On the other hand, at the beginning of the introduction the reader is assumed to know what a cohomology ring is or to click on the link to learn this first. Then why explaining the easier definitions instead of just linking them? 132.230.30.102 (talk) 16:25, 18 February 2016 (UTC)[reply]