This book is an introduction to fiber bundles and fibrations. But
the ultimate goal is to make the reader feel comfortable with basic
ideas in homotopy theory. The author found that the classification
of principal fiber bundles is an ideal motivation for this purpose.
The notion of homotopy appears naturally in the classification.
Basic tools in homotopy theory such as homotopy groups and their
long exact sequence need to be introduced. Furthermore, the notion
of fibrations, which is one of three important classes of maps in
homotopy theory, can be obtained by extracting the most essential
properties of fiber bundles. The book begins with elementary
examples and then gradually introduces abstract definitions when
necessary. The reader is assumed to be familiar with point-set
topology, but it is the only requirement for this book.
General
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