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Algebraic Topology A First Course
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ISBN
:
9788184891249
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Publisher
:
Springer (sie)
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Subject
:
Encyclopaedias & Reference Works
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Binding
:
Hardcover
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Pages
:
448
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Year
:
2009
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1190.0
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856.0
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Description
This book introduces the important ideas of algebraic topology by emphasizing the relation of topological Ideas with other areas of mathematics Rather than choosing one point of view of modern topology (homotopy theory, axiomatic homology, or differential topology, say), the author concentrates on concrete problems in spaces of low dimension. Introducing only as much algebraic machinery as necessary for the problems encountered. This makes it possible to see a wider variety of important features in the subject than is common in introductory texts: it is also in harmony with the historical development of the subject The book is aimed at students who do not necessarily Intend on specializing in algebraic topology. The first part of the book emphasizes relations with calculus and uses notions from calculus to prove the Jordan curve theorem. The study of fundamental groups and covering spaces emphasizes group actions. A section on the topology of surfaces includes applications to Riemann surfaces and algebraic curves. A final section gives a taste of generalizations to higher dimensions.
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