Qualifying Examination
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چکیده
2. (T) Let CPn be complex projective n-space. (a) Describe the cohomology ring H∗(CPn,Z) and, using the Kunneth formula, the cohomology ring H∗(CPn × CPn,Z). (b) Let ∆ ⊂ CPn×CPn be the diagonal, and δ = i∗[∆] ∈ H2n(CP×CP,Z) the image of the fundamental class of ∆ under the inclusion i : ∆ → CPn × CPn. In terms of your description of H∗(CPn × CPn,Z) above, find the Poincaré dual δ∗ ∈ H2n(CPn × CPn,Z) of δ.
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