Group Actions on Spaces of Rational Functions
Kohhei Yamaguchi
University of Electro-Communications, Tokyo, JapanYohei Ono
University of Electro-Communications, Tokyo, Japan

Abstract
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. 173–181
DOI 10.2977/PRIMS/1145476152