J an 2 00 3 COMBINATORIAL CONDITIONS THAT IMPLY WORD - HYPERBOLICITY FOR 3 - MANIFOLDS
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چکیده
Thurston conjectured that a closed triangulated 3-manifold in which every edge has degree 5 or 6, and no two edges of degree 5 lie in a common 2-cell, has word-hyperbolic fundamental group. We establish Thurston's conjecture by proving that such a manifold admits a piece-wise Euclidean metric of non-positive curvature and the universal cover contains no isometrically embedded flat planes. The proof involves a mixture of computer computation and techniques from small cancellation theory.
منابع مشابه
Combinatorial Conditions That Imply Word-hyperbolicity for 3-manifolds
Thurston conjectured that a closed triangulated 3-manifold in which every edge has degree 5 or 6, and no two edges of degree 5 lie in a common 2-cell, has word-hyperbolic fundamental group. We establish Thurston’s conjecture by proving that such a manifold admits a piecewise Euclidean metric of non-positive curvature and the universal cover contains no isometrically embedded flat planes. The pr...
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تاریخ انتشار 2003