Fiber Bundles and Homotopy

Dai Tamaki (Autor)

Buch | Hardcover

350 Seiten

2021
World Scientific Publishing Co Pte Ltd (Verlag)
978-981-12-3799-7 (ISBN)

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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.

Preface; Bundling Spaces Together; Covering Spaces as Bundles; Basics of Fiber Bundles; Classification of Fiber Bundles; Fibrations; Postscript; Appendix:The Meaning of Compact-Open Topology; Vector Bundles; Simplicial Techniques;

Erscheinungsdatum	21.06.2021
Verlagsort	Singapore
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	981-12-3799-9 / 9811237999
ISBN-13	978-981-12-3799-7 / 9789811237997
Zustand	Neuware