Hatcher-Algebraic-Topology · Problem 2C.3

Cohomology

Mathematics — Graph Theory · complex-projective-space-fixed-point-free

Problem

Verify that the formula

f(z_1, \ldots, z_{2k}) = (\bar{z}_2, -\bar{z}_1, \bar{z}_4, -\bar{z}_3, \ldots, \bar{z}_{2k}, -\bar{z}_{2k-1})

defines a map

f: \mathbb{C}^{2k} \to \mathbb{C}^{2k}

inducing a quotient map

\mathbb{C}P^{2k-1} \to \mathbb{C}P^{2k-1}

without fixed points.