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I calculated the cohomology of $\mathbb{C}P^{n}$ using the spectral sequence associate to the fibration $S^{1} \hookrightarrow S^{2n+1} \rightarrow \mathbb{C}P^{n}$. How can I find the first Chern class in this way?

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The first Chern class of what? Chern classes are associated to vector bundles. –  Paul VanKoughnett Feb 2 '13 at 20:18
I have to find the first Chern class looking at this bundle... –  ArthurStuart Feb 2 '13 at 20:29
you seem to be asking a lot of questions that look like homework... and are poorly phrased. –  Sean Tilson Feb 13 '13 at 14:37
@PaulVanKoughnett: Hi! –  Sean Tilson Feb 13 '13 at 14:38
@SeanTilson: whatUP –  Paul VanKoughnett Feb 14 '13 at 5:29

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