- CiteKey: “Gon99” - Type: journalArticle - Title: “Volumes of hyperbolic manifolds and mixed Tate motives,” - Author: “Goncharov, Alexander;” - Year: 1996 - DOI: 10.48550/arXiv.alg-geom/9601021 - Collections: “Syllabus; Talbot 2022,”
Volumes of hyperbolic manifolds and mixed Tate motives
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- URL: https://arxiv.org/abs/alg-geom/9601021v3
- URI: http://zotero.org/users/1049732/items/WTFMS2RL
- Open in Zotero: Zotero
Abstract
Two different constructions of an invariant of an odd dimensional hyperbolic manifold in the K-group \(K_{2n-1}(\mkern 1.5mu\overline{\mkern-1.5mu\Bbb \mkern-1.5mu}\mkern 1.5muQ)\otimes \Bbb Q\) 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.