Geometry and topology
John O'Connor
CONTENTS
Introduction
Foundations
The linear groups
Examples of linear groups
Isometries of
R
^{n}
Isometries of the line
Isometries of the plane
Isometries in 3 dimensions
Symmetry groups in the plane
Frieze groups
Platonic solids
Finite rotation groups of
R
^{3}
Full finite symmetry groups in
R
^{3}
Affine geometry
Affine theorems
Similarity geometry
Projective spaces
Homogeneous coordinates
The projective groups
More projective groups
Some theorems in plane projective geometry
Introduction to topology
Surfaces
The Connected Sum
Planar models
The Euler Characteristic
The Classification Theorem
Summary of results
Geometry quotations
More geometry quotations
Exercises
Exercises 1
Exercises 2
Exercises 3
Exercises 4
Exercises 5
Exercises 6
Exercises 7
Exercises 8
Exercises 9
JOC MT4521 Geometry and topology: February 2010
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