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This introduction to some basic ideas in algebraic topology is devoted to the foundations and applications of homology theory. After the essentials of singular homology and some important applications are given, successive topics covered include attaching spaces, finite CW complexes, cohomology products, manifolds, Poincare duality, and fixed point theory. This second edition includes a chapter on covering spaces and many new exercises.
The 20 years since the publication of this book have been an era of continuing growth and development in the field of algebraic topology. New generations of young mathematicians have been trained, and classical problems have been solved, particularly through the application of geometry and knot theory. Diverse new resources for introductory coursework have appeared, but there is persistent interest in an intuitive treatment of the basic ideas. This second edition has been expanded through the addition of a chapter on covering spaces. By analysis of the lifting problem it introduces the funda mental group and explores its properties, including Van Kampen's Theorem and the relationship with the first homology group. It has been inserted after the third chapter since it uses some definitions and results included prior to that point. However, much of the material is directly accessible from the same background as Chapter 1, so there would be some flexibility in how these topics are integrated into a course. The Bibliography has been supplemented by the addition of selected books and historical articles that have appeared since 1973.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
The 20 years since the publication of this book have been an era of continuing growth and development in the field of algebraic topology. New generations of young mathematicians have been trained, and classical problems have been solved, particularly through the application of geometry and knot theory. Diverse new resources for introductory coursework have appeared, but there is persistent interest in an intuitive treatment of the basic ideas. This second edition has been expanded through the addition of a chapter on covering spaces. By analysis of the lifting problem it introduces the funda mental group and explores its properties, including Van Kampen's Theorem and the relationship with the first homology group. It has been inserted after the third chapter since it uses some definitions and results included prior to that point. However, much of the material is directly accessible from the same background as Chapter 1, so there would be some flexibility in how these topics are integrated into a course. The Bibliography has been supplemented by the addition of selected books and historical articles that have appeared since 1973.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.