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Graduate Texts in Mathematics

Classical Topology and Combinatorial Group Theory

Authors: Stillwell, John

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About this Textbook

In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does not understand the simplest topological facts, such as the reason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical developĀ­ ment where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recrea. ions like the seven bridges; rather, it resulted from the visualization of problems from other parts of mathematicsĀ­ complex analysis (Riemann), mechanics (poincare), and group theory (Oehn). It is these connections to other parts of mathematics which make topology an important as well as a beautiful subject.

Table of contents (9 chapters)

Table of contents (9 chapters)

Buy this book

eBook $74.99
price for USA in USD (gross)
  • ISBN 978-1-4684-0110-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Classical Topology and Combinatorial Group Theory
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
72
Copyright
1980
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York Inc.
eBook ISBN
978-1-4684-0110-3
DOI
10.1007/978-1-4684-0110-3
Series ISSN
0072-5285
Edition Number
1
Topics