Topics on Riemann Surfaces and Fuchsian Groups

doi:10.1017/CBO9780511569272

Presents a cross-section of different aspects of Riemann surfaces, introducing the reader to the basics as well as highlighting new developments in the field. It provides a mixture of classical material, recent results and some non-mainstream topics. The book is based on lectures from the conference Topics on Riemann Surfaces and Fuchsian Groups held in Madrid to mark the 25th anniversary of the Universidad Nacional de Educación a Distancia. For those wishing to pursue research in this area, this volume offers a valuable summary of contemporary thought and a source of fresh geometric and algebraic insights. The book will be suitable for graduate courses, as well as providing a useful reference for those already working in geometry, group theory, complex analysis, algebraic geometry, topology and theoretical physics.

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Topics on Riemann Surfaces and Fuchsian Groups

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Introduction
pp ix-xiv

The geometry of Riemann surfaces
pp 1-28

Introduction arithmetic of Fuchsian groups
pp 29-42

Riemann surfaces, Belyi functions and hypermaps
pp 43-68

Compact Riemann surfaces and algebraic function fields
pp 69-90

Symmetries of Riemann surfaces from a combinatorial point of view
pp 91-112

Compact Klein surfaces and real algebraic curves
pp 113-132

Moduli spaces of real algebraic curves
pp 133-154

Period matrices and the Schottky problem
pp 155-164

Hurwitz spaces
pp 165-177

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