JournalsprimsVol. 39, No. 1pp. 173–181

Group Actions on Spaces of Rational Functions

  • Kohhei Yamaguchi

    University of Electro-Communications, Tokyo, Japan
  • Yohei Ono

    University of Electro-Communications, Tokyo, Japan
Group Actions on Spaces of Rational Functions cover
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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