This e-book includes a whole facts of the truth that Borel's regulator map is two times Beilinson's regulator map. the method of the evidence follows the argument sketched in Beilinson's unique paper and is determined by very related descriptions of the Chern-Weil morphisms and the van Est isomorphism. The publication has diversified components. the 1st one experiences the fabric from algebraic topology and Lie team conception wanted for the comparability theorem. themes resembling simplicial gadgets, Hopf algebras, attribute periods, the Weil algebra, Bott's Periodicity theorem, Lie algebra cohomology, non-stop crew cohomology and the van Est Theorem are mentioned. the second one half includes the comparability theorem and the explicit fabric wanted in its facts, similar to particular descriptions of the Chern-Weil morphism and the van Est isomorphisms, a dialogue approximately small cosimplicial algebras, and a comparability of other definitions of Borel's regulator.
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