منابع مشابه
Volumes of hyperbolic Haken manifolds , I
Introduction In [14] a program was initiated for using the topological theory of 3manifolds to obtain lower bounds for volumes of hyperbolic 3-manifolds. In [1], by a combination of new geometric ideas with relatively standard (but specifically 3-dimensional) topological techniques, we showed that every closed, orientable hyperbolic 3-manifold whose first Betti number is at least 3 has volume e...
متن کاملVolumes of Hyperbolic Haken Manifolds, Ii
We show that if M is a closed hyperbolic 3-manifold and if π1(M) has a non-abelian free quotient, then the volume of M is greater than 0.92. If, in addition, π1(M) contains no genus-2 surface groups, then the volume of M is greater than 1.02. Using these results we show that if there are infinitely many primitive homology classes in H2(M ; Z) which are not represented by fibroids, then the volu...
متن کاملOn volumes of hyperbolic 3-manifolds
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 μ : K•(BG)→ K•(C ∗ redG) for our class of manifolds, and then classify μ in terms of the ideals in the ring of integers of a quadratic number field K. Next, ...
متن کاملLower Bounds on Volumes of Hyperbolic Haken 3-manifolds
In this paper, we find lower bounds for the volumes of certain hyperbolic Haken 3manifolds. The theory of Jorgensen and Thurston shows that the volumes of hyperbolic 3-manifolds are well-ordered, but no one has been able to find the smallest one. The best known result for closed manifolds is that the smallest closed hyperbolic 3-manifold has volume > 0.16668, proven by Gabai, Meyerhoff, and Thu...
متن کاملVolumes of hyperbolic manifolds and mixed Tate motives
1. Volumes of (2n − 1)-dimensional hyperbolic manifolds and the Borel regulator on K2n−1(Q). Let M be an n-dimensional hyperbolic manifold with finite volume vol(M). If n = 2m is an even number, then by the Gauss-Bonnet theorem ([Ch]) vol(M) = −c2m · χ(M) where c2m = 1/2×(volume of sphere S of radius 1) and χ(M) is the Euler characteristic of M. This is straightforward for compact manifolds and...
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ژورنال
عنوان ژورنال: Journal of Differential Geometry
سال: 1983
ISSN: 0022-040X
DOI: 10.4310/jdg/1214438182