Poetry Madness
 
 

Recently Viewed clear list


Interviews | March 17, 2014

Shawn Donley: IMG Peter Stark: The Powells.com Interview



Peter StarkIt's hard to believe that 200 years ago, the Pacific Northwest was one of the most remote and isolated regions in the world. In 1810, four years... Continue »
  1. $19.59 Sale Hardcover add to wish list

spacer
Qualifying orders ship free.
$82.75
New Trade Paper
Ships in 1 to 3 days
Add to Wishlist
available for shipping or prepaid pickup only
Available for In-store Pickup
in 7 to 12 days
Qty Store Section
25 Remote Warehouse Mathematics- Differential Geometry

This title in other editions

Princeton Landmarks in Mathematics & Physics #0014: The Topology of Fibre Bundles. (PMS-14)

by

Princeton Landmarks in Mathematics & Physics #0014: The Topology of Fibre Bundles. (PMS-14) Cover

 

Synopses & Reviews

Publisher Comments:

Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically.

It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.

Book News Annotation:

The seventh printing and first paper edition of the introduction to a subject that is now an integral part of differential geometry and important in such aspects of modern physics as gauge theory. Begins with a general introduction to bundles, with discussions of such topics as differentiable manifolds and covering spaces. Then surveys a number of advanced topics, including homotopy theory and cohomology theory, and uses them to study the properties of fiber bundles further.
Annotation c. Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically.

It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.

Description:

Includes bibliographical references (p. 223-227) and index.

Table of Contents

Part I. THE GENERAL THEORY OF BUNDLES

1. Introduction 3

2. Coordinate bundles and fibre bundles 6

3. Construction of a bundle from coordinate transformations 14

4. The product bundle 16

5. The Ehresmann-Feldbau definition of bundle 18

6. Differentiable manifolds and tensor bundles 20

7. Factor spaces of groups 28

8. The principal bundle and the principal map 35

9. Associated bundles and relative bundles 43

10. The induced bundle 47

11. Homotopies of maps of bundles 49

12. Construction of cross-sections 54

13. Bundles having a totally disconnected group 59

14. Covering spaces 67

Part II. THE HOMOTOPY THEORY OF BUNDLES

15. Homotopy groups 72

16. The operations of Pi1 on Pi n 83

17. The homotopy sequence of a bundle 90

18. The classification of bundles over the n-sphere 96

19. Universal bundles and the classification theorem 100

20. The fibering of spheres by spheres 105

21. The homotopy groups of spheres 110

22. Homotopy groups of the orthogonal groups 114

23. A characteristic map for the bundle Rn+1 over S n 118

24. A characteristic map for the bundle Un over S 2n - 1 124

25. The homotopy groups of miscellaneous manifolds 131

26. Sphere bundles over spheres 134

27. The tangent bundle of S n 140

28. On the non-existence of fiberings of spheres by spheres 144

Part III. THE COHOMOLOGY THEORY OF BUNDLES

29. The stepwise extension of a cross-section 148

30. Bundles of coefficients 151

31. Cohomology groups based on a bundle of coefficients 155

32. The obstruction cocycle 166

33. The difference cochain 169

34. Extension and deformation theorems 174

35. The primary obstruction and the characteristic cohomology class 177

36. The primary difference of two cross-sections 181

37. Extensions of functions, and the homotopy classification of maps 184

38. The Whitney characteristic classes of a sphere bundle 190

39. The Stiefel characteristic classes of differentiable manifolds 199

40. Quadratic forms on manifolds 204

41. Complex analytic manifolds and exterior forms of degree 2 209

Appendix 218

Bibliography 223

Index 228

Product Details

ISBN:
9780691005485
Author:
Steenrod, Norman
Publisher:
Princeton University Press
Location:
Princeton, N.J.
Subject:
Advanced
Subject:
Geometry - Differential
Subject:
Topology
Subject:
Fiber bundles (mathematics)
Subject:
Fiber bundles
Subject:
Mathematics
Subject:
Mathematics-Differential Geometry
Copyright:
Edition Description:
Trade paper
Series:
Princeton Landmarks in Mathematics & Physics
Series Volume:
0014
Publication Date:
April 1999
Binding:
TRADE PAPER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
224
Dimensions:
9 x 6 in 12 oz

Other books you might like

  1. The Rufus Chronicle: Another Autumn Used Trade Paper $4.95
  2. Wrinkle in Time Used Mass Market $2.95
  3. Little Schubert Used Trade Paper $1.50
  4. 123 Used Hardcover $2.50
  5. Janice VanCleave's Play and Find Out... Used Trade Paper $5.50
  6. 123 to the Zoo Used Hardcover $6.95

Related Subjects

Children's » Animals » Animal Stories » General
Children's » General
Religion » Comparative Religion » General
Science and Mathematics » Mathematics » Differential Geometry
Science and Mathematics » Physics » General

Princeton Landmarks in Mathematics & Physics #0014: The Topology of Fibre Bundles. (PMS-14) New Trade Paper
0 stars - 0 reviews
$82.75 In Stock
Product details 224 pages Princeton University Press - English 9780691005485 Reviews:
"Synopsis" by , Fibre bundles, now an integral part of differential geometry, are also of great importance in modern physics--such as in gauge theory. This book, a succinct introduction to the subject by renown mathematician Norman Steenrod, was the first to present the subject systematically.

It begins with a general introduction to bundles, including such topics as differentiable manifolds and covering spaces. The author then provides brief surveys of advanced topics, such as homotopy theory and cohomology theory, before using them to study further properties of fibre bundles. The result is a classic and timeless work of great utility that will appeal to serious mathematicians and theoretical physicists alike.

spacer
spacer
  • back to top
Follow us on...




Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at Powells.com.