Algebraic Topology: A First Course (Graduate Texts in

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Algebraic Topology: A First Course (Graduate Texts in Mathematics, 153)

To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the reÂ 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, differÂ ential topology, etc.), we concentrate our attention on concrete probÂ lems in low dimensions, introducing only as much algebraic machinÂ 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 topolÂ ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical develÂ opment of the subject. What would we like a student to know after a first course in toÂ 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: underÂ standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; windÂ ing numbers and degrees of mappings, fixed-point theorems; appliÂ cations such as the Jordan curve theorem, invariance of domain; inÂ dices of vector fields and Euler characteristics; fundamental groups
Country USA
Brand Springer
Manufacturer Springer
Binding Paperback
ItemPartNumber 13 Illustrations, black and white; XVIII
ReleaseDate 1997-09-05
UnitCount 1
EANs 9780387943275

Country	USA
Brand	Springer
Manufacturer	Springer
Binding	Paperback
ItemPartNumber	13 Illustrations, black and white; XVIII
ReleaseDate	1997-09-05
UnitCount	1
EANs	9780387943275

Algebraic Topology: A First Course (Graduate Texts in Mathematics, 153)

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