2003/05/22 by Igor Nikolaev, Nikolaev, Igor
Mathematics · #46L85 #57M50 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.math/0305316
openalex publication_date 2003/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.