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Cohomology — Allen Hatcher
Mathematics — Topology · complex-projective-space-fixed-point-free
Problem Verify that the formula f ( z 1 , ⋯ , z 2 k ) = ( z ˉ 2 , − z ˉ 1 , z ˉ 4 , − z ˉ 3 , ⋯ , z ˉ 2 k , − z ˉ 2 k − 1 ) f(z_1, \cdots, z_{2k}) = (\bar{z}_2, -\bar{z}_1, \bar{z}_4, -\bar{z}_3, \cdots, \bar{z}_{2k}, -\bar{z}_{2k-1}) f ( z 1 , ⋯ , z 2 k ) = ( z ˉ 2 , − z ˉ 1 , z ˉ 4 , − z ˉ 3 , ⋯ , z ˉ 2 k , − z ˉ 2 k − 1 ) f : C 2 k → C 2 k f: \mathbb{C}^{2k} \to \mathbb{C}^{2k} f : C 2 k → C 2 k C P 2 k − 1 → C P 2 k − 1 \mathbb{CP}^{2k-1} \to \mathbb{CP}^{2k-1} CP 2 k − 1 → CP 2 k − 1 Browse the problem library