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) = 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.
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© 1966 Dale Hausemoller
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Husemoller, D. (1966). Relative K-Theory. In: Fibre Bundles. Graduate Texts in Mathematics, vol 20. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4008-0_9
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DOI: https://doi.org/10.1007/978-1-4757-4008-0_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-4010-3
Online ISBN: 978-1-4757-4008-0
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