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We prove that an irreducible 3-manifold with fundamental groupthat satisfies a certain group-theoretic property called RFRSis virtually fibered. As a corollary, we show that 3-dimensionalreflection orbifolds and arithmetic hyperbolic orbifolds definedby a quadratic form virtually fiber. These include the SeifertWeber dodecahedral space and the Bianchi groups. Moreover, weshow that a taut-sutured compression body has a finite-sheetedcover with a depth one taut-oriented foliation. Received July 29, 2007. 相似文献
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Ian Agol 《Geometriae Dedicata》2003,102(1):53-64
In this paper we prove the Cheeger inequality for infinite weighted graphs endowed with 'corresponding' measure. This measure has already been developed in the study of tree lattices. Our graphs have finite volumes. A similar theory has already been developed for manifolds of finite volumes. 相似文献
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Ian Agol Joel Hass William Thurston 《Transactions of the American Mathematical Society》2006,358(9):3821-3850
We show that the problem of deciding whether a polygonal knot in a closed three-dimensional manifold bounds a surface of genus at most is NP-complete. We also show that the problem of deciding whether a curve in a PL manifold bounds a surface of area less than a given constant is NP-hard.
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Ian Agol Peter A. Storm William P. Thurston with an appendix by Nathan Dunfield 《Journal of the American Mathematical Society》2007,20(4):1053-1077
We prove a volume inequality for 3-manifolds having metrics ``bent' along a surface and satisfying certain curvature conditions. The result makes use of Perelman's work on the Ricci flow and geometrization of closed 3-manifolds. Corollaries include a new proof of a conjecture of Bonahon about volumes of convex cores of Kleinian groups, improved volume estimates for certain Haken hyperbolic 3-manifolds, and a lower bound on the minimal volume of orientable hyperbolic 3-manifolds. An appendix compares estimates of volumes of hyperbolic 3-manifolds drilled along a closed embedded geodesic with experimental data.
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