Timeline for Construction of the Stiefel-Whitney and Chern Classes
Current License: CC BY-SA 2.5
6 events
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| Apr 6, 2010 at 20:44 | comment | added | Dan Ramras | How hard is it to show that the classes you define this way are the ordinary SW classes? You seem to indicate that you do it by showing that these obstruction-type classes satisfy the axioms. I remember Greg Brumfiel once saying that Hassler Whitney considered the Whitney Sum Theorem to be the hardest thing he ever proved; the point being, it's hard to check that the obstruction classes satisfy the axioms. Having heard that, I've never tried it for myself... I suppose this may be hidden somewhere in Steenrod's book, but not in the nice language you're using here. | |
| Apr 1, 2010 at 19:45 | history | edited | Dev Sinha | CC BY-SA 2.5 |
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| Apr 1, 2010 at 5:58 | history | edited | Dev Sinha | CC BY-SA 2.5 |
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| Apr 1, 2010 at 5:58 | comment | added | Dev Sinha | First, note that this can just be done smoothly, etc. Transition maps are always maps from U \int V --> GL_n(R). But now since U \int V is the intersection of two simplices (I'll edit to specify that), it is itself some simplex and has a linear structure, and I want this map to GL_n(R) to be linear. On needs this to define a `piecewise linear section' - otherwise what looks linear over one simplex might not look linear to neighbor on their overlap. | |
| Apr 1, 2010 at 5:35 | comment | added | Dan Ramras | Can you explain what you mean when you say that the transition maps are linear? In some sense, transition maps for vector bundles are always linear... But you presumably mean something else, having to do with the simplicial structure on the base space? | |
| Apr 1, 2010 at 5:04 | history | answered | Dev Sinha | CC BY-SA 2.5 |