We discuss a natural refinement, of the classical construction of the Euler characteristic of a perfect complex of modules. In this article we discuss a natural refinement of the classical notion of Euler characteristic. This refined construction combines the standard algebraic construction of the Euler characteristic of a perfect complex of modules with an equivariant version of aspects of the classical construction of Whitehead torsion [25, 29]. It can be applied to any perfect complex of modules that is endowed with certain additional structure of a cohomologieaJ nature and takes values in a suitable relative algebraic A"-group (which is itself the target of a natural homomorphism from an appropriate Whitehead group).
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