CLOSED 3–MANIFOLDS UNCHANGED BY DEHN SURGERY
CLOSED 3–MANIFOLDS UNCHANGED BY DEHN SURGERY
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闭合 3——DEHN 手术未改变歧管
DOI：
10.1142/s0218216592000161
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发表时间：
1992
影响因子：
0.5
通讯作者：
Y. Mathieu
中科院分区：
文献类型：
--
作者：
Y. Mathieu
如果X是三叶纽结的空间，我们可以找到，对于每个整数e，∂X，ρe，γe上的两个斜率，使得ρ填充X(γe)和X(Dehn E)是同胚的3-流形。手术的核心是带有同胚互补的不等价纽结。如果X是2桥环结的结空间，则可以得到类似的结果。在阿托罗同调球面中，纽结由它们的补码确定当且仅当双曲纽结是。
If X is the space of the trefoil knot, we can find, for every integer e, two slopes on ∂X, ρe, γe, such that the Dehn fillings X (ρe) and X (γe) are homeomorphic 3-manifolds. The cores of the surgeries are inequivalent knots with homeomorphic complements. Analogous results are available if X is the knotspace of a 2-bridge torus knot. In an atoroidal homology sphere knots are determined by their complement if and only if hyperbolic knots are.