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Jul 16 '13 at 22:11 history edited Ricardo Andrade CC BY-SA 3.0
correct minor typos
Jul 16 '13 at 21:02 answer András Szűcs timeline score: 2
Sep 30 '10 at 15:07 comment added Dylan Wilson @Scott- Apologies; it felt spammy to post two such highly related questions in the span of a few minutes.
Sep 30 '10 at 8:24 comment added S. Carnahan Dylan, if you have a new question, you should submit it as a new question, rather than writing over the old one.
Sep 30 '10 at 6:20 answer Christian Nassau timeline score: 7
Sep 30 '10 at 5:22 comment added Dylan Wilson @Paul- Got it! I'll have to look at the paper then. Looks like this question has been answered. And your assumption was wrong :), I didn't even know what characteristic classes were until about 6 hours ago... so this is all new and fascinating. @Daniel- Those look GREAT! Thank you very much! (I'm looking at the 2001 version; is that the most current?)
Sep 30 '10 at 3:51 answer Dev Sinha timeline score: 3
Sep 30 '10 at 3:48 comment added Daniel Pomerleano THere are some pretty great notes by Haynes Miller called "Notes on Cobordism" that explain all of this and more.
Sep 30 '10 at 3:27 comment added Paul I mean Thom determines, not the numbers! For any sequence $(n_1, n_2, n_3,..n_k)$ where $n_1 +2n_2+3n_3+...+kn_k=d$, you get a Stiefel whitney number of a d dimensional manifold by evaluating w_1^n_1 U ... U w_k^n_k on the fundamental class. The collection of {0,1} you get from all such "partions" of d give a monomorphism $Omega_d\to Z/2^p$, i.e. they determine the bordism class for a given manifold. But this need not be onto; eg for d=1, p=1. Thom determined the image.
Sep 30 '10 at 1:56 comment added Dylan Wilson Also: Is there any way to fix the typo in my question title without needlessly bumping up my post?
Sep 30 '10 at 1:55 comment added Dylan Wilson I'm confused: "Stiefel-whitney numbers... determine which numbers occur." The numbers determine themselves?
Sep 29 '10 at 23:11 comment added Paul I'll assume you already know that Thom's original paper both proves that the Stiefel Whitney numbers determine the unoriented bordism class and also determines which numbers occur. Take a look at WIkipedia's "cobordism" page.
Sep 29 '10 at 23:04 comment added Dylan Wilson Whoops, I put "classes" when I meant "numbers." I don't know if your comment would give a necessary condition for when some sequence of zeros and ones can be realized as the Stiefel-Whitney numbers of some manifold. Would it?
Sep 29 '10 at 23:02 history edited Dylan Wilson CC BY-SA 2.5
edited body
Sep 29 '10 at 21:20 history edited Dylan Wilson CC BY-SA 2.5
typo fixed in title
Sep 29 '10 at 21:00 answer Oscar Randal-Williams timeline score: 5
Sep 29 '10 at 20:56 history asked Dylan Wilson CC BY-SA 2.5