Abstract
Abstract We present an infinite series formula based on the Karoubi–Hamida integral, for the universal Borel class evaluated on H 2n+1(GL(ℂ)). For a cyclotomic field F we define a canonical set of elements in K 3(F) and present a novel approach (based on a free differential calculus) to constructing them. Indeed, we are able to explicitly construct their images in H 3(GL(ℂ)) under the Hurewicz map. Applying our formula to these images yields a value V 1(F), which coincides with the Borel regulator R 1(F) when our set is a basis of K 3(F) modulo torsion. For F = ℚ(e 2πi/3) a computation of V 1(F) has been made based on our techniques.
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