Irreducible SL(2, C)-metabelian representations of branched twist spins
Irreducible SL(2, C)-metabelian representations of branched twist spins
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分支扭曲自旋的不可约 SL(2, C)-元变表示
DOI：
10.1142/s021821651950007x
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发表时间：
2018
影响因子：
0.5
通讯作者：
Fukuda Mizuki
中科院分区：
文献类型：
--
作者：
久水俊和;石原比伊呂;中井裕子;生駒孝臣;大薮海;芳澤元;池和田有紀;松永和浩;田中奈保;高鳥廉;大澤泉;田村航;豊永聡美;森田大介;木下昌規;水野嶺;井出麻衣子;岩崎悟;Fukuda Mizuki
A-分支扭曲自旋是由A-结和互质整数和决定的纤维结。对于a-纽结，Nagato证明了a-纽结的纽结群的不可约亚交换表示的共轭类的个数由-纽结的纽结行列式决定。本文通过比较分支扭转自旋的纽结群的表示和Lin的纽结群的表示，证明了到共轭为止，分支扭转自旋的纽结群的不可约亚标量表示数是由轨道空间中伴随纽结的行列式决定的。
An-branched twist spin is a fibered-knot inwhich is determined by a-knotand coprime integersand. For a-knot, Nagasato proved that the number of conjugacy classes of irreducible-metabelian representations of the knot group of a-knot is determined by the knot determinant of the-knot. In this paper, we prove that the number of irreducible-metabelian representations of the knot group of an-branched twist spin is determined up to conjugation by the determinant of the associated-knot in the orbit space by comparing a presentation of the knot group of the branched twist spin with the Lin’s presentation of the knot group of the-knot.