On volumes of hyperbolic 3-manifolds

Details On volumes of hyperbolic 3-manifolds On volumes of hyperbolic 3-manifolds

2003-05-22

arxiv.org/abs/math/0305316v1

Mathematics

Geometric Topology

18 pages, research report

Scientific paper

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.

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