On volumes of hyperbolic 3-manifolds
Geometric Topology
2016-09-07 v1 Operator Algebras
Abstract
The main thrust of present note is a volume formula for hyperbolic surface bundle with the fundamental group G. The novelty consists in a purely algebraic approach to the above problem. Initially, we concentrate on the Baum-Connes morphism m(G): K(BG)--> K(C*G) for our class of manifolds, and then classify m(G) in terms of the ideals in the ring of integers of a quadratic number field K. Next, we extract the topological data (e.g. volume of the orbifold H/G) from the arithmetic of field K.
Keywords
Cite
@article{arxiv.math/0305316,
title = {On volumes of hyperbolic 3-manifolds},
author = {Igor Nikolaev},
journal= {arXiv preprint arXiv:math/0305316},
year = {2016}
}
Comments
18 pages, research report