Graduate Texts in Mathematics

Topology and Geometry

Authors: Bredon, Glen E.

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About this Textbook

The golden age of mathematics-that was not the age of Euclid, it is ours. C. J. KEYSER This time of writing is the hundredth anniversary of the publication (1892) of Poincare's first note on topology, which arguably marks the beginning of the subject of algebraic, or "combinatorial," topology. There was earlier scattered work by Euler, Listing (who coined the word "topology"), Mobius and his band, Riemann, Klein, and Betti. Indeed, even as early as 1679, Leibniz indicated the desirability of creating a geometry of the topological type. The establishment of topology (or "analysis situs" as it was often called at the time) as a coherent theory, however, belongs to Poincare. Curiously, the beginning of general topology, also called "point set topology," dates fourteen years later when Frechet published the first abstract treatment of the subject in 1906. Since the beginning of time, or at least the era of Archimedes, smooth manifolds (curves, surfaces, mechanical configurations, the universe) have been a central focus in mathematics. They have always been at the core of interest in topology. After the seminal work of Milnor, Smale, and many others, in the last half of this century, the topological aspects of smooth manifolds, as distinct from the differential geometric aspects, became a subject in its own right.

Reviews

G.E. Bredon

Topology and Geometry

"An interesting and original graduate text in topology and geometry. The topics covered include . . . general topology, smooth manifolds, homology and homotopy groups, duality, cohomology and products . . . a good lecturer can use this text to create a fine course at the appropriate level . . . There are various innovative things, which are accessible but not traditionally covered. A beginning graduate student can use this text to learn a great deal of mathematics."—MATHEMATICAL REVIEWS


Table of contents (7 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-1-4757-6848-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.95
price for USA
  • ISBN 978-0-387-97926-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $79.95
price for USA
  • ISBN 978-1-4419-3103-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Topology and Geometry
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
139
Copyright
2002
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-6848-0
DOI
10.1007/978-1-4757-6848-0
Hardcover ISBN
978-0-387-97926-7
Softcover ISBN
978-1-4419-3103-0
Series ISSN
0072-5285
Edition Number
1
Number of Pages
XXIII, 131
Topics