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. More refined tools are developed in a chapter on winding number, and an appendix gives a glimpse of knot theory. Moreover, in this revised edition, a new section gives a geometrical description of part of the Classification Theorem for surfaces. Several striking new pictures show how given a sphere with any number of ordinary handles and at least one Klein handle, all the ordinary handles can be converted into Klein handles.

Numerous examples and exercises make this a useful textbook for a first undergraduate course in topology, providing a firm geometrical foundation for further study. For much of the book the prerequisites are slight, though, so anyone with curiosity and tenacity will be able to enjoy the Aperitif.

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