Fibre Bundles pp 110-127 | Cite as

# Relative *K*-Theory

Chapter

## 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.

## Keywords

Exact Sequence Vector Bundle Fibre Bundle Group Morphism Cohomology Theory
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

© Dale Hausemoller 1966