A representation of closed, orientable 3-manifolds as 3-fold branched coverings of $S^3$
A representation of closed, orientable 3-manifolds as 3-fold branched coverings of $S^3$
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将闭合、可定向 3 流形表示为 $S^3$ 的 3 倍分支覆盖层
DOI：
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发表时间：
1974
期刊：
影响因子：
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通讯作者：
J. Montesinos
中科院分区：
文献类型：
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作者：
J. Montesinos
所表示的链路是S中的链路L以及链路群TT（S-L）到d个符号的对称置换群Sf，的表示。让我们称co为单的，如果它通过适当的换位表示L的每一条子午线。若（L，co）是一个表示环，则存在一个唯一相伴的闭可定向3-流形M（L，co），即S在L上分支的d-重覆盖，它由表示co决定。亚历山大[1]证明了每个闭可定向3-流形对某个环L和表示ω是M（L，ω）。M.希尔登（给作者的个人通信）证明，
A represented link is a link L in S together with a representation œ of the link group TT(S—L) into the symmetric permutation group of d symbols Sf^. Let us call co simple if it represents each meridian of L by an appropriate transposition. If (L, co) is a represented link, there is a uniquely associated closed, orientable 3-manifold M(L, co), namely the d-fold covering of S branched over L, that is determined by the representation co. It has been proved by J. W. Alexander [1] that every closed orientable 3-manifold is M(L, co)for some link L and representation co. H. M. Hilden (personal communication to the author) has proved