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revised Examples of common false beliefs in mathematics
The space shuttle discovery is on display in Virginia. The shuttle the author is referring to is most likely Challenger, and the Rogers Commission which Feynman was a part of.
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revised Colimits in the category of smooth manifolds
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comment Completion of a category
So if the construction $DM(\mathbb{C})$ given below doesn't give a complete and cocomplete category into which $\mathbb{C}$ embeds, is there a different construction which does do this?
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revised $(BU,f)$ structures on manifolds via stable normal bundles and stable tangent bundles
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comment $(BU,f)$ structures on manifolds via stable normal bundles and stable tangent bundles
Johannes, thank you so much. You are of course correct; I see it now. Thanks for the help!
Sep
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comment $(BU,f)$ structures on manifolds via stable normal bundles and stable tangent bundles
I've also never heard the term "concordant" used. Do you mean it in the sense here: ncatlab.org/nlab/show/concordance ?
Sep
5
comment $(BU,f)$ structures on manifolds via stable normal bundles and stable tangent bundles
Is there just an extra $\oplus$ in the displayed equation? When you pick the embedding $\iota$, are you assuming the almost complex structure on $V\oplus \mathbb{R}^r$ is induced from the standard almost complex structure on $\mathbb{C}^n$? I don't think this can always be done. Consider the example in the question, $X=pt$, with $X\times\mathbb{C}$ and the almost complex structure given by $x+iy\to y-ix$; it is not the restriction of the standard complex structure on $\mathbb{C}^n$ for any embedding $\mathbb{C}\rightarrow\mathbb{C}$. I agree that this works for stable complex vector bundles.
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comment Open Problems in Algebraic Topology and Homotopy Theory
Dylan, that is perfect! Thanks!
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