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Fibre Bundles pp 122-139 | Cite as

Relative K-Theory

  • Dale Husemoller
Part of the Graduate Texts in Mathematics book series (GTM, volume 20)

Abstract

We define a collapsing or trivialization procedure for bundles over X which yields a bundle over X / A for a closed subset A of X. With this construction we are able to give alternative descriptions of \(K(X,A) = \tilde K(X/A).\). For a finite CW-pair (X, A) we can define an exact sequence K(A) ← K(X) ← K(X, A) ← K(S(A)) ← K(S(X)), using an appropriate “coboundary operator.” With this sequence we see that in some sense the K-cofunctor can be used to define a cohomology theory.

Keywords

Exact Sequence Vector Bundle Group Morphism Cohomology Theory Natural Morphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Dale Husemoller
    • 1
  1. 1.Department of MathematicsHaverford CollegeHaverfordUSA

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