On Cyclic Groups of Automorphisms of Riemann Surfaces
نویسنده
چکیده
The question of extendability of the action of a cyclic group of automorphisms of a compact Riemann surface is considered. Particular attention is paid to those cases corresponding to Singerman's list of Fuchsian groups which are not nitely-maximal, and more generally to cases involving a Fuchsian triangle group. The results provide partial answers to the question of which cyclic groups are the full automorphism group of some Riemann surface of given genus g > 1.
منابع مشابه
On automorphisms groups of cyclic p-gonal Riemann surfaces
In this work we obtain the group of conformal and anticonformal automorphisms of real cyclic p-gonal Riemann surfaces, where p ≥ 3 is a prime integer and the genus of the surfaces is at least (p − 1) + 1. We use Fuchsian and NEC groups, and cohomology of finite groups.
متن کاملOn Riemann surfaces of genus g with 4g automorphisms
We determine, for all genus g ≥ 2 the Riemann surfaces of genus g with exactly 4g automorphisms. For g 6= 3, 6, 12, 15 or 30, this surfaces form a real Riemann surface Fg in the moduli space Mg: the Riemann sphere with three punctures. We obtain the automorphism groups and extended automorphism groups of the surfaces in the family. Furthermore we determine the topological types of the real form...
متن کاملAutomorphisms of Riemann Surfaces
This paper consists of mainly two parts. First it is a survey of some results on automorphisms of Riemann surfaces and Fuchsian groups. A theorem of Hurwitz states that the maximal automorphism group of a compact Riemann surface of genus 9 has order at most 84(g-1). It is well-known that the Klein quartic is the unique genus 3 curve that attains the Hurwitz bound. We will show in the second par...
متن کاملEla Dihedral Groups of Automorphisms of Compact Riemann Surfaces of Genus Two
In this short note, the conjugacy classes of finite dihedral subgroups of the 4 × 4 integral symplectic group are considered. A complete list of representatives of the classes is obtained, among them six classes are realizable by analytic automorphisms of compact connected Riemann surfaces of genus two.
متن کاملComplex Hyperbolic Manifolds Homotopy Equivalent to a Riemann Surface
We construct actions of fundamental groups of Riemann surfaces by automorphisms of the complex hyperbolic plane, which realize all possible values of Toledo's invariant. For integer values of these actions are discrete embeddings. The quotient complex hyperbolic surfaces are disc bundles over Riemann surfaces, whose topological type is determined in terms of .
متن کامل