Symmetries of Compact Riemann Surfaces (Lecture Notes in Mathematics, Vol. 2007) (Lecture Notes in Mathematics, 2007)

Symmetries of Compact Riemann Surfaces
	Preface
	Contents
	Introduction
		Chapter:1 Preliminaries
			1.1 NEC Groups and Their Signatures
			1.2 Normal Subgroups of NEC Groups
			1.3 Centralizers of Reflections
			1.4 Uniformization and Automorphism Groups of Riemann and Klein Surfaces
				1.4.1 Maximal NEC Groups
				1.4.2 Teichmüller Spaces
			1.5 Symmetric Riemann Surfaces
				1.5.1 Algebraic Conditions
		Chapter:2 On the Number of Conjugacy Classes of Symmetries of Riemann Surfaces
			2.1 Conjugacy Classes of Involutions in 2-Groups
			2.2 Symmetries with Non-Empty Set of Fixed Points
			2.3 Symmetries with Empty Set of Fixed Points
			2.4 Symmetries of Surfaces Admitting a Fixed Point Free Symmetry
		Chapter:3 Counting Ovals of Symmetries of Riemann Surfaces
			3.1 Enumeration of Ovals of Symmetries at Large
			3.2 Total Number of Ovals of Non-Conjugate Symmetries
			3.3 Total Number of Ovals of all Symmetries of a Riemann Surface
			3.4 Total Number of Ovals of a Couple of Symmetries
		Chapter:4 Symmetry Types of Some Families of Riemann Surfaces
			4.1 Symmetry Type of the Riemann Sphere
			4.2 Symmetry Types of Tori
				4.2.1 Symmetric Tori
			4.3 Symmetry Types of Hyperelliptic Riemann Surfaces
				4.3.1 A Geometric Method
				4.3.2 An Example
		Chapter:5 Symmetry Types of Riemann Surfaces with a Large Group of Automorphisms
			5.1 Some General Results
			5.2 Symmetry Types of Macbeath--Singerman Surfaces
			5.3 Symmetry Types of Accola--Maclachlan and Kulkarni Surfaces
				5.3.1 Number of Ovals of the Symmetries
				5.3.2 Separating Character of the Symmetries
			5.4 Algebraic Formulae for the Symmetries
		Chapter:
6 Appendix
			6.1 Compact Riemann Surfaces Without Symmetries
		References
		Index