Algebraic Topology (eBook)

A First Course

William Fulton (Autor)

eBook Download: PDF

2013
Springer New York (Verlag)
978-1-4612-4180-5 (ISBN)

Infos

To 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 not 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 know after a first course in to- pology (assuming we reject the answer: half of what one would like the student to know 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

Produkt-Details

• Erscheint lt. Verlag: 1.12.2013
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 1-4612-4180-4 / 1461241804
• ISBN-13: 978-1-4612-4180-5 / 9781461241805