Abstract
Let \mathrm{Hol}_d be the space consisting of all holomorphic maps f : S^2 → S^2 of degree d . The group \mathrm{Hol}_1 = \mathrm{PSL}_2(ℂ) acts on \mathrm{Hol}_d freely by the post-composition and we shall study the orbit space X_d = \mathrm{Hol}_1\backslash \mathrm{Hol}_d . As an application, we shall determine the homotopy types of the universal covering spaces of \mathrm{Hol}_d and X_d explicitly.
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