Diffeomorphisms and automorphisms of compact hyperbolic 2-orbifolds

Summary

Introductory remarks

This paper, a sequel to [E], owes its existence to the 2007 conference for Bill Harvey. In his lecture on the opening day, Gabino González-Diez mentioned an example from a remark in [E]. Later he asked me about its proof, which is not given in [E]. Theorem 1.1 restates the example, and Appendix I provides the missing proof.

Most of the paper explores connections between [E] and the interesting papers [MH] by Maclachlan and Harvey and [BH1] and [BH2] by Birman and Hilden. Some of their results about homeomorphisms of Riemann surfaces have analogues for diffeomorphisms of two-dimensional compact hyperbolic orbifolds. These are stated below as corollaries of Theorems 1.2 and 1.3. It seems appropriate to include them here because both Harvey and Maclachlan were present at the conference.

The main result, Theorem 1.2, is proved here twice. One proof uses Theorem 1 of [E], which depends on ideas from [EE] and [ES]. The other, in Appendix III, relies on [DE] and [EM]. The papers [DE], [EE], [EM], and [ES] are collaborations with four different coauthors. I am indebted to them all. Two of them, Jim Eells and Adrien Douady, are no longer with us. I dedicate this paper to their memories.