Volumes of hyperbolic manifolds and mixed Tate motives
Author:
Alexander Goncharov
Journal:
J. Amer. Math. Soc. 12 (1999), 569-618
MSC (1991):
Primary 11Gxx; Secondary 19Fxx, 57-XX
DOI:
https://doi.org/10.1090/S0894-0347-99-00293-3
MathSciNet review:
1649192
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Two different constructions of an invariant of an odd-dimensional hyperbolic manifold with values in $K_{2n-1}(\overline {\mathbb Q})\otimes \mathbb Q$ are given. We prove that the volume of the manifold equals the value of the Borel regulator on this invariant. The scissors congruence groups in noneuclidean geometries are studied and related to mixed Tate motives and algebraic K-theory of $\mathbb C$. We contribute to the general theory of mixed Hodge structures by introducing for Hodge-Tate structures the big period map with values in $\mathbb C \otimes \mathbb C^*(n-2)$.
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Additional Information
Alexander Goncharov
Affiliation:
Department of Mathematics, Brown University, Providence, Rhode Island 02912
Email:
sasha@math.brown.edu
Received by editor(s):
October 16, 1996
Received by editor(s) in revised form:
October 11, 1998
Article copyright:
© Copyright 1999
American Mathematical Society