The Casson-Walker invariant for branched cyclic covers of Ssp 3 branched over a doubled knot
The Casson-Walker invariant for branched cyclic covers of Ssp 3 branched over a doubled knot
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Ssp 3 在双结上分支的分支循环覆盖的 Casson-Walker 不变量
DOI：
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发表时间：
1997
影响因子：
0.4
通讯作者：
Katsuhiro Ishibe
中科院分区：
文献类型：
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作者：
Katsuhiro Ishibe
1985年，A. Casson利用基本群在SU（2）中的表示定义了定向积分同调3球的不变量λ [1]。K.把它推广到有理同调3-球面的不变量。步行者[11]. 1993年，C. Lescop [9]给出了一个计算有理同调3-球面的不变量的公式，当它们由框架连接表示时，并表明它自然地扩展到所有3-流形的不变量。设L是S中的一个环，L是S的n重循环分支覆盖.定义λn（L）= λ（L）。然后λn成为一个不变量的链接。对于对偶纽结、环面纽结和迭代环面纽结，A. Davidow（见[3]，[4]）计算了n重分支覆盖的Casson整数不变量，当n.对于任何链接，D. Mullins [10]成功地计算了2重分支覆盖的Casson-Walker有理值不变量，当Y？L是一个有理同调球面。本文利用C. Lescop公式和D. Mullins，我们将计算的Casson-Walker不变量的分支循环覆盖的S3分支上的m-扭曲的双结。我们将证明下列定理和推论。
In 1985, A. Casson defined an invariant λ for oriented integral homology 3spheres by using representations from their fundamental group into SU{2) [1]. It was extended to an invariant for rational homology 3-spheres by K. Walker [11]. In 1993, C. Lescop [9] gave a formula to calculate this invariant for rational homology 3-spheres when they are presented by framed links and showed that it naturally extends to an invariant for all 3-manifolds. Let L be a link in S and let Σ£ be its n-fold cyclic branched cover. Define λn(L) = λ(Σ£). Then λn becomes an invariant of links. For doubles of knots, torus knots and iterated torus knots, A. Davidow (see [3], [4]) calculated Casson's integer invariant for n-fold branched covers, when Σ •£• is an integral homology sphere. For any links, D. Mullins [10] have succeeded in calculating Casson-Walker's rational valued invariant for 2-fold branched covers, when Y?L is a rational homology sphere. In this paper, using C. Lescop's formula and the result of D. Mullins, we will calculate the Casson-Walker invariant for branched cyclic covers of S 3 branched over the m-twisted double of a knot. We will show the following theorem and corollary.