Volumes of hyperbolic manifolds and mixed Tate motives
Abstract
Two different constructions of an invariant of an odd dimensional hyperbolic manifold in the K-group K2n-1( Q) Q are given. The volume of the manifold is equal to the value of the Borel regulator on that element. The scissor congruence groups in non euclidian geometries are studied and their relationship with algebraic K-theory of the field of complex numbers is discussed.
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