JP Journal of Geometry and Topology
Volume 8, Issue 2, Pages 129 - 150
(July 2008)
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STABLE INVERSES OF VECTOR BUNDLES
AND
K-THEORY
Elena A. Kudryavtseva (Russia), Kalathoor Varadarajan (Canada) and Peter Zvengrowski (Canada)
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Certain foundational questions of K-theory,
such as the existence of a stable (additive) inverse for a given
-vector bundle and the surjectivity of the natural map
are investigated for spaces X
that are paracompact but not necessarily connected or finite dimensional as well
as for
-vector bundles over X that need not
have constant rank. For
we show that the natural map
is not surjective using elementary
techniques. More explicitly, we show
that
is not in the image of the map
where
is the quotient map. We also show
that countable direct products of finite CW-complexes need not have the homotopy
type of a CW-complex.
