Computing Borel's Regulator

Details Computing Borel's Regulator Computing Borel's Regulator

2009-08-26

arxiv.org/abs/0908.3765v4

Mathematics

K-Theory and Homology

25 pages, merging of Part I with Part II (arXiv:0909.0883) and major changes

Scientific paper

We present an infinite series formula based on the Karoubi-Hamida integral, for the universal Borel class evaluated on H_{2n+1}(GL(\mathbb{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. Applying our computer algorithm to this set yields a value V_1(F), which coincides with the Borel regulator R_1(F) when our set is a basis modulo torsion. For F= \mathbb{Q}(e^{2\pi i/3}) we compute V_1(F).

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