Computing Borel's regulator
Choo, Zacky; Mannan, Wajid; Sánchez-García, Rubén J.; Snaith, Victor P.
2015-01-01 00:00:00
Abstract We present an infinite series formula based on the Karoubi–Hamida integral, for the universal Borel class evaluated on H 2 n +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 2π i /3 ) a computation of V 1 ( F ) has been made based on our techniques.
http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.pngForum Mathematicumde Gruyterhttp://www.deepdyve.com/lp/de-gruyter/computing-borel-s-regulator-2BO0WZxeQ2
Abstract We present an infinite series formula based on the Karoubi–Hamida integral, for the universal Borel class evaluated on H 2 n +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 2π i /3 ) a computation of V 1 ( F ) has been made based on our techniques.
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