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The Topology of Fibre Bundles
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Norman Steenrod
Language:
English
Published/Copyright:
1951
About this book
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.
Author / Editor information
Norman Steenrod was a professor of Mathematics at Princeton University and a member of the National Academy Of Sciences. He also edited Reviews in Topology.
Topics
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Frontmatter
i -
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Preface
v -
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Contents
vii -
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Part I. The General Theory of Bundles
1 -
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Part II. The Homotopy Theory of Bundles
72 -
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Part III. The Cohomology Theory of Bundles
148 -
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Appendix
218 -
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Bibliography
223 -
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Index
228
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 2, 2016
eBook ISBN:
9781400883875
Pages and Images/Illustrations in book
Main content:
224
eBook ISBN:
9781400883875
Keywords for this book
Fiber bundle; Homotopy; Subgroup; Homotopy group; Topology; Tangent bundle; Principal bundle; Coordinate system; Equivalence class; Special case; Topological group; Theorem; Cohomology; Homology (mathematics); Homeomorphism; Vector field; Coset; Division algebra; Connected space; Identity element; Classification theorem; Product topology; Inclusion map; Cyclic group; Inner automorphism; Associated bundle; Cohomology ring; Quaternion; Differentiable manifold; N-sphere; Transitive relation; Jacobian matrix and determinant; Linear space (geometry); Simplicial complex; Lie group; Tietze extension theorem; Coefficient; Bundle map; Subset; Automorphism; Universal bundle; Homomorphism; Dimension (vector space); Algebraic topology; Associative algebra; Determinant; Line segment; Line element; Atlas (topology); Hurewicz theorem; Stiefel manifold; Topological space; Linear map; Metric tensor; Mapping cylinder; Orthogonalization; Klein bottle; Euler number; Conjugacy class; Tensor; Subalgebra; Transpose; Natural topology; Hopf theorem; Permutation; Invariant subspace; Differential structure; Equivalence relation; Lattice of subgroups; Barycentric subdivision
Audience(s) for this book
College/higher education;Professional and scholarly;
