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About this product
- DescriptionTo the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re- lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ- ential topology, etc.), we concentrate our attention on concrete prob- lems in low dimensions, introducing only as much algebraic machin- ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are t aiming to become practicing algebraic topol- ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel- opment of the subject. What would we like a student to kw after a first course in to- pology (assuming we reject the answer: half of what one would like the student to kw after a second course in topology)? Our answers to this have guided the choice of material, which includes: under- standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind- ing numbers and degrees of mappings, fixed-point theorems; appli- cations such as the Jordan curve theorem, invariance of domain; in- dices of vector fields and Euler characteristics; fundamental groups
- Author(s)William Fulton
- PublisherSpringer-Verlag New York Inc.
- Date of Publication05/09/1997
- Series TitleGraduate Texts in Mathematics
- Series Part/Volume Numberv.153
- Place of PublicationNew York, NY
- Country of PublicationUnited States
- ImprintSpringer-Verlag New York Inc.
- Content Note13 black & white illustrations, biography
- Weight1390 g
- Width156 mm
- Height234 mm
- Spine23 mm
- Format DetailsTrade paperback (US)
- Edition Statement1st ed. 1995. Corr. 2nd printing 1997
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