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Computing Borel's Regulator

Computing Borel's Regulator
Computing Borel's Regulator
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 R1(F) when our
set is a basis of K_3(F) modulo torsion. For F = Q(e^{2?i/3}) a computation of V_1(F) has
been made based on our techniques.
Borel Regulator
0933-7741
29pp
Choo, Zacky
c9a47b10-ec6d-446d-b246-0256135ae075
Mannan, Wajid
60b6458b-ec92-460f-80e4-bf3b6fd54f56
Garcia-Sanchez, Ruben J.
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Snaith, Victor P.
29688768-1068-409f-9861-50ad28cd0524
Choo, Zacky
c9a47b10-ec6d-446d-b246-0256135ae075
Mannan, Wajid
60b6458b-ec92-460f-80e4-bf3b6fd54f56
Garcia-Sanchez, Ruben J.
8246cea2-ae1c-44f2-94e9-bacc9371c3ed
Snaith, Victor P.
29688768-1068-409f-9861-50ad28cd0524

Choo, Zacky, Mannan, Wajid, Garcia-Sanchez, Ruben J. and Snaith, Victor P. (2012) Computing Borel's Regulator. Forum Mathematicum, 29pp. (In Press)

Record type: Article

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 R1(F) when our
set is a basis of K_3(F) modulo torsion. For F = Q(e^{2?i/3}) a computation of V_1(F) has
been made based on our techniques.

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More information

Accepted/In Press date: 15 June 2012
Keywords: Borel Regulator

Identifiers

Local EPrints ID: 206595
URI: https://eprints.soton.ac.uk/id/eprint/206595
ISSN: 0933-7741
PURE UUID: 83b798d4-00e5-46ef-ad10-5bf8c5a10d25
ORCID for Ruben J. Garcia-Sanchez: ORCID iD orcid.org/0000-0001-6479-3028

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Date deposited: 10 Jan 2012 10:58
Last modified: 06 Jun 2018 12:33

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