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arxiv: math/0101138 · v4 · pith:OJ5H6K6Tnew · submitted 2001-01-17 · 🧮 math.GT · math.DG

Volume change under drilling

classification 🧮 math.GT math.DG
keywords volumehyperbolicgeodesicmanifoldchangeclosedcomplementcomplete
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Given a hyperbolic 3-manifold M containing an embedded closed geodesic, we estimate the volume of a complete hyperbolic metric on the complement of the geodesic in terms of the geometry of M. As a corollary, we show that the smallest volume orientable hyperbolic 3-manifold has volume >.32 .

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