Groups and Geometry

Roger C. Lyndon

• Publisher: Cambridge University Press
• Year: 1985
• Print ISBN: 9780521316941
• eBook ISBN: 9781107108011
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

This book, which was originally published in 1985 and has been translated and revised by the author from notes of a course, is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-known connections between the two subjects and, whilst keeping the presentation at a level that assumes only a basic background in mathematics, leads the reader to the frontiers of current research at the time of publication. The treatment is concrete and combinatorial with a minimal use of analytic geometry. In the interest of the reader's intuition, most of the geometry considered is two-dimensional and there is an emphasis on examples, both in the text and in the problems at the end of each chapter.

Table of contents

• Cover
• Series Page
• Title
• Copyright
• PREFACE
• CONTENTS
• CHAPTER ONE: SYMMETRIES AND GROUPS
• CHAPTER TWO: ISOMETRIES OF THE EUCLIDEAN PLANE
• CHAPTER THREE: SUBGROUPS OF THE GROUP OF ISOMETRIES OF THE PLANE
• CHAPTER FOUR: DISCONTINUOUS GROUPS OF ISOMETRIES OF THE EUCLIDEAN PLANE: PLANE CRYSTALLOGRAPHIC GROUPS
• CHAPTER FIVE: REGULAR TESSELLATIONS IN HIGHER DIMENSIONS
• CHAPTER SIX: INCIDENCE GEOMETRY OF THE AFFINE PLANE
• CHAPTER SEVEN: PROJECTIVE GEOMETRY
• CHAPTER EIGHT: INVERSIVE GEOMETRY
• CHAPTER NINE: HYPERBOLIC GEOMETRY
• CHAPTER TEN: FUCHSIAN GROUPS
• REFERENCES
• INDEX