Displaying similar documents to “Realizing countable groups as automorphism groups of Riemann surfaces.”

A Cartan-type result for invariant distances and one-dimensional holomorphic retracts.

Colum Watt (2001)

Publicacions Matemàtiques

Similarity:

We derive conditions under which a holomorphic mapping of a taut Riemann surface must be an automorphism. This is an analogue involving invariant distances of a result of H. Cartan. Using similar methods we prove an existence result for 1-dimensional holomorphic retracts in a taut complex manifold.

Automorphisms of Riemann surfaces with two fixed points

Tomasz Szemberg (1991)

Annales Polonici Mathematici

Similarity:

We give an upper bound for the order of an automorphism of a Riemann surface with two fixed points. The main results are presented in Theorems 1.4 and 2.4.

Conformal actions with prescribed periods on Riemann surfaces

G. Gromadzki, W. Marzantowicz (2011)

Fundamenta Mathematicae

Similarity:

It is a natural question what is the set of minimal periods of a holomorphic maps on a Riemann surface of negative Euler characteristic. Sierakowski studied ordinary holomorphic periods on classical Riemann surfaces. Here we study orientation reversing automorphisms acting on classical Riemann surfaces, and also automorphisms of non-orientable unbordered Klein surfaces to which, following Singerman, we shall refer to as non-orientable Riemann surfaces. We get a complete set of conditions...

Theory of coverings in the study of Riemann surfaces

Ewa Tyszkowska (2012)

Colloquium Mathematicae

Similarity:

For a G-covering Y → Y/G = X induced by a properly discontinuous action of a group G on a topological space Y, there is a natural action of π(X,x) on the set F of points in Y with nontrivial stabilizers in G. We study the covering of X obtained from the universal covering of X and the left action of π(X,x) on F. We find a formula for the number of fixed points of an element g ∈ G which is a generalization of Macbeath's formula applied to an automorphism of a Riemann surface. We give...

A family of M-surfaces whose automorphism groups act transitively on the mirrors.

Adnan Melekoglu (2000)

Revista Matemática Complutense

Similarity:

Let X be a compact Riemmann surface of genus g > 1. A symmetry T of X is an anticonformal involution. The fixed point set of T is a disjoint union of simple closed curves, each of which is called a mirror of T. If T fixes g +1 mirrors then it is called an M-symmetry and X is called an M-surface. If X admits an automorphism of order g + 1 which cyclically permutes the mirrors of T then we shall call X an M-surface with the M-property. In this paper we investigate those M-surfaces...