منابع مشابه
Geometrization of 3-dimensional Coxeter orbifolds and Singer’s conjecture
Associated to any Coxeter system (W,S), there is a labeled simplicial complex L and a contractible CW-complex ΣL (the Davis complex) on which W acts properly and cocompactly. ΣL admits a cellulation under which the nerve of each vertex is L. It follows that if L is a triangulation of S, then ΣL is a contractible n-manifold. In this case, the orbit space, KL := ΣL/W , is a Coxeter orbifold. We p...
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A 3-dimensional orbifold is a metrizable space with coherent local models given by quotients of R by finite subgroups of O(3). For example, the quotient of a 3-manifold by a properly discontinuous group action naturally inherits a structure of a 3-orbifold. Such an orbifold is said to be very good when the group action is finite. For a general background about orbifolds see [BS1,2], [DaM], [Sc]...
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A three-dimensional closed orientable orbifold (with no bad suborbifolds) is known to have a geometric decomposition from work of Perelman [50, 51] in the manifold case, along with earlier work of Boileau-Leeb-Porti [4], Boileau-Maillot-Porti [5], BoileauPorti [6], Cooper-Hodgson-Kerckhoff [19] and Thurston [59]. We give a new, logically independent, unified proof of the geometrization of orbif...
متن کاملGeometrization of 3-dimensional Coxeter group manifolds and Singer’s conjecture
Associated to any Coxeter system (W,S), there is a labeled simplicial complex L and a contractible CW-complex ΣL (the Davis complex) on which W acts properly and cocompactly. ΣL admits a cellulation under which the nerve of each vertex is L. It follows that if L is a triangulation of S , then ΣL is a contractible n-manifold. We prove that a special case of the Singer conjecture for ΣL (on the v...
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The computer programs SnapPea by Weeks and Geo by Casson have proven to be powerful tools in the study of hyperbolic 3-manifolds. Manifolds are special examples of spaces called orbifolds, which are modelled locally on R modulo finite groups of symmetries. SnapPea can also be used to study orbifolds but it is restricted to those whose singular set is a link. One goal of this thesis is to lay do...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2005
ISSN: 0003-486X
DOI: 10.4007/annals.2005.162.195