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Isolated Exceptional Dehn Surgeries On Hyperbolic Knots

机译:孤立的双曲线结异常Dehn手术

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摘要

For a hyperbolic knot in the 3-sphere, at most finitely many Dehn surgeries yield non-hyperbolic manifolds. Such exceptional surgeries are classified into four types, lens space surgery, small Seifert fibered surgery, toroidal surgery and reducing surgery, according to the resulting manifolds. For each of the three types except reducing surgery, we give infinitely many hyperbolic knots with integral exceptional Dehn surgeries of the given type, whose adjacent integral surgeries are not exceptional.
机译:对于3球中的双曲线结,最多只能有限地进行许多Dehn手术,产生非双曲线流形。根据产生的歧管,这种特殊的手术分为四种类型:晶状体手术,小型Seifert纤维手术,环形手术和缩小手术。对于这三种类型中的每一种,除了减少手术之外,我们都会给定类型的无数次Dehn外科手术,无数次双曲线打结,其相邻的整体性外科手术也不例外。

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