# Volumes of hyperbolic manifolds and mixed Tate motives

@article{Goncharov1996VolumesOH,
title={Volumes of hyperbolic manifolds and mixed Tate motives},
author={A. Goncharov},
journal={Journal of the American Mathematical Society},
year={1996},
volume={12},
pages={569-618}
}
• A. Goncharov
• Published 1996
• Mathematics
• Journal of the American Mathematical Society
• 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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