## chern classes of a trivial bundle [closed]

Could someone explain to me why the chern classes of a trivial bundle are zero? (i'm studying it from Bott Tu book)

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You should probably ask this on math.stackexchange.com – Mariano Suárez-Alvarez Jan 18 2012 at 19:23
either follow Mariano's suggestion or use a flat connection :) – Stefan Waldmann Jan 18 2012 at 19:25
(Bott and Tu do not define Chern classes using connections, though) – Mariano Suárez-Alvarez Jan 18 2012 at 19:39
It's a sum of line bundles, and... – Allen Knutson Jan 18 2012 at 19:52
As stated in Bott-Tu, consider the fact that $P(E) = M \times P(V)$ for trivial bundles. What is the cohomology of a product of spaces? – Simon Rose Jan 18 2012 at 19:53