Ebook: A Topological Aperitif

This is a book of elementary geometric topology, in which geometry, frequently illustrated, guides calculation. The book starts with a wealth of examples, often subtle, of how to be mathematically certain whether two objects are the same from the point of view of topology.

After introducing surfaces, such as the Klein bottle, the book explores the properties of polyhedra drawn on these surfaces. Even in the simplest case, of spherical polyhedra, there are good questions to be asked. More refined tools are developed in a chapter on winding number, and an appendix gives a glimpse of knot theory.

There are many examples and exercises making this a useful textbook for a first undergraduate course in topology. For much of the book the prerequisites are slight, though, so anyone with curiosity and tenacity will be able to enjoy the book. As well as arousing curiosity, the book gives a firm geometrical foundation for further study.

"A Topological Aperitif provides a marvellous introduction to the subject, with many different tastes of ideas."

Professor Sir Roger Penrose OM FRS, Mathematical Institute, Oxford, UK

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This is a book of elementary geometric topology, in which geometry, frequently illustrated, guides calculation. The book starts with a wealth of examples, often subtle, of how to be mathematically certain whether two objects are the same from the point of view of topology.

After introducing surfaces, such as the Klein bottle, the book explores the properties of polyhedra drawn on these surfaces. Even in the simplest case, of spherical polyhedra, there are good questions to be asked. More refined tools are developed in a chapter on winding number, and an appendix gives a glimpse of knot theory.

There are many examples and exercises making this a useful textbook for a first undergraduate course in topology. For much of the book the prerequisites are slight, though, so anyone with curiosity and tenacity will be able to enjoy the book. As well as arousing curiosity, the book gives a firm geometrical foundation for further study.

"A Topological Aperitif provides a marvellous introduction to the subject, with many different tastes of ideas."

Professor Sir Roger Penrose OM FRS, Mathematical Institute, Oxford, UK

Content:
Front Matter....Pages i-ix
Homeomorphic Sets....Pages 1-15
Topological Properties....Pages 17-27
Equivalent Subsets....Pages 29-59
Surfaces and Spaces....Pages 61-76
Polyhedra....Pages 77-102
Winding Number....Pages 103-115
Continuity....Pages 117-124
Knots....Pages 125-132
History....Pages 133-138
Solutions....Pages 139-162
Back Matter....Pages 163-166

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This is a book of elementary geometric topology, in which geometry, frequently illustrated, guides calculation. The book starts with a wealth of examples, often subtle, of how to be mathematically certain whether two objects are the same from the point of view of topology.

After introducing surfaces, such as the Klein bottle, the book explores the properties of polyhedra drawn on these surfaces. Even in the simplest case, of spherical polyhedra, there are good questions to be asked. More refined tools are developed in a chapter on winding number, and an appendix gives a glimpse of knot theory.

There are many examples and exercises making this a useful textbook for a first undergraduate course in topology. For much of the book the prerequisites are slight, though, so anyone with curiosity and tenacity will be able to enjoy the book. As well as arousing curiosity, the book gives a firm geometrical foundation for further study.

"A Topological Aperitif provides a marvellous introduction to the subject, with many different tastes of ideas."

Professor Sir Roger Penrose OM FRS, Mathematical Institute, Oxford, UK

Content:
Front Matter....Pages i-ix
Homeomorphic Sets....Pages 1-15
Topological Properties....Pages 17-27
Equivalent Subsets....Pages 29-59
Surfaces and Spaces....Pages 61-76
Polyhedra....Pages 77-102
Winding Number....Pages 103-115
Continuity....Pages 117-124
Knots....Pages 125-132
History....Pages 133-138
Solutions....Pages 139-162
Back Matter....Pages 163-166
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