| Circle Bundle |
Article Index for Circle |
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Information AboutCircle Bundle |
| CATEGORIES ABOUT CIRCLE BUNDLE | |
| fiber bundles | |
| k-theory | |
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RELATIONSHIP TO ELECTRODYNAMICS
Given a circle bundle ''P'' over ''M'' and its projection : one has the Homomorphism
CLASSIFICATION The Isomorphism Class es of circle bundles over a manifold ''M'' are in one-to-one correspondence with the elements of the second Integral Cohomology Group of ''M''. This isomorphism is realized by the Euler Class . Equivalently, the isomorphism classes correspond to homotopy classes of maps to the infinite-dimensional Complex Projective Space , which is the classifying space of U(1) . See Classifying Space For U(n) .
See also: Wang Sequence . |
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