Let Hol_d_ be the space consisting of all holomorphic maps f : S_2 → S_2 of degree d. The group Hol1 = PSL2(ℂ) acts on Hol_d freely by the post-composition and we shall study the orbit space Xd = Hol1\Hol_d. As an application we shall determine the homotopy types of the universal covering spaces of Hol_d_ and Xd explicitly.
Cite this article
Kohhei Yamaguchi, Yohei Ono, Group Actions on Spaces of Rational Functions. Publ. Res. Inst. Math. Sci. 39 (2003), no. 1, pp. 173–181DOI 10.2977/PRIMS/1145476152