Volumes of hyperbolic manifolds and mixed Tate motives

Details Volumes of hyperbolic manifolds and mixed Tate motives Volumes of hyperbolic manifolds and mixed Tate motives

1996-01-19

arxiv.org/abs/alg-geom/9601021v3

Mathematics

Algebraic Geometry

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Scientific paper

Two different constructions of an invariant of an odd dimensional hyperbolic manifold in the K-group $K_{2n-1}(\bar \Bbb Q)\otimes \Bbb Q$ 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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