The modulo 2 homology group of the space of rational functions
The cohomology group \(H_*(F_ k^*({\mathbb{S}}^ 2,{\mathbb{C}}{\mathbb{P}}^ m);{\mathbb{Z}}_ 2)\) of the space of based holomorphic maps of degree k from \({\mathbb{S}}^ 2\) to \({\mathbb{C}}{\mathbb{P}}^ m\) is considered. A series of theorems concerning certain elements of \(H_*(F_ k^*({\mathbb{S}}^ 2,{\mathbb{C}}{\mathbb{P}}^ m);{\mathbb{Z}}_ 2)\), produced by the loop sum and Dyer- Lashof operation, are proved. It is shown for different values of k and m that the elements considered are the basis of \(H_*(F_ k^*({\mathbb{S}}^ 2,{\mathbb{C}}{\mathbb{P}}^ m);{\mathbb{Z}}_ 2)\).
scientific article; zbMATH DE number 4153470
scientific article