The aim of this note is to give an axiomatic and elementary treatment of Chern-characters of vector bundles with values in a class of cohomology-theories arising in topology and algebra. Given a theory of Chern-classes for complex vector bundles with values in singular cohomology one gets in a natural way a Chern-character from complex K-theory to singular cohomology using the projective bundle theorem and the Newton polynomials. The Chern-classes of a complex vector bundle may be defined using the notion of an Euler class and one may prove that a theory of Chern-classes with values in singular cohomology is unique. In this note it is shown one may relax the conditions on the theory for Chern-classes and still get a Chern character. Hence the Chern-character depends on some choices.
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