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Computing Borel's regulator

Computing Borel's regulator 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.png Forum Mathematicum de Gruyter

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Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2012-0064
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 2015

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