Geometry and topology

John O'Connor

CONTENTS

Introduction

  1. Foundations
  2. The linear groups
  3. Examples of linear groups
  4. Isometries of Rn
  5. Isometries of the line
  6. Isometries of the plane
  7. Isometries in 3 dimensions
  8. Symmetry groups in the plane
  9. Frieze groups
  10. Platonic solids
  11. Finite rotation groups of R3
  12. Full finite symmetry groups in R3
  13. Affine geometry
  1. Affine theorems
  2. Similarity geometry
  3. Projective spaces
  4. Homogeneous coordinates
  5. The projective groups
  6. More projective groups
  7. Some theorems in plane projective geometry
  8. Introduction to topology
  9. Surfaces
  10. The Connected Sum
  11. Planar models
  12. The Euler Characteristic
  13. The Classification Theorem

Summary of results

Geometry quotations
More geometry quotations
Exercises
  1. Exercises 1
  2. Exercises 2
  3. Exercises 3
  4. Exercises 4
  5. Exercises 5
  1. Exercises 6
  2. Exercises 7
  3. Exercises 8
  4. Exercises 9
JOC MT4521 Geometry and topology: February 2010