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Algebraic Topology: An Intuitive Approach (Translations of Mathematical Monographs)
The single most difficult thing one faces when one begins to learn a new branch of mathematics is to get a feel for the mathematical sense of the subject. The purpose of this book is to help the aspiring reader acquire this essential common sense about algebraic topology in a short period of time. To this end, Sato leads the reader through simple but
meaningful examples in concrete terms. Moreover, results are not discussed in their greatest possible generality, but in terms of the simplest and most essential cases. In response to suggestions from readers of the original edition of this book, Sato has added an appendix of useful definitions and results on sets, general topology, groups and such. He has also provided references. Topics covered include fundamental notions such as homeomorphisms, homotopy equivalence, fundamental groups and higher homotopy groups, homology and cohomology, fiber bundles, spectral sequences and characteristic classes. Objects and examples considered in the text include the torus, the Mobius strip, the Klein bottle, closed surfaces, cell complexes and vector bundles.
Contents:
Objectives
- Homeomorphisms and homotopy equivalences
- Topological spaces and cell complexes
- Fundamental groups and higher homotopy groups
- Homology
- Homology groups of cell complexes
- Cohomology
- Homology of product spaces and the universal coefficient theorem
- Fiber bundles and vector bundles
- Spectral sequences
- A view from current mathematics
- Appendix
- Answers to exercises
- Recommended reading
- Index
Brief Description:
The purpose of this book is to help the aspiring reader acquire an essential common sense about algebraic topology in a short period of time. The author leads readers through simple but meaningful examples in concrete terms and results are discussed in terms of the most essential cases.
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