4-fold symmetric quandle invariants of 3-manifolds
4-fold symmetric quandle invariants of 3-manifolds
复制标题
3 流形的 4 重对称 qudle 不变量
DOI：
10.1016/j.topol.2011.02.006
复制
发表时间：
2011
影响因子：
0.7
通讯作者：
Takefumi Nosaka
中科院分区：
文献类型：
--
作者：
Tetsuya Ijiri;Masahiro Shinya;Kimitaka Nakazawa;中村元;中村元;中村元;T. Nosaka E. Hatakenaka;Takefumi Nosaka;Takefumi Nosaka
对于四边形X，定义四边形空间BX，修改Fenn，Rourke和Sanderson（1995）[13]的齿条空间，并在Z[π2（BX）]中定义链接的四边形同伦不变量，修改Fenn，Rourke和Sanderson（1995）[13]的齿条同伦不变量。众所周知，Carter 等人引入的共循环不变量。 (2005) [3]，卡特等人。 (2003) [5]，卡特等人。 (2001) [6] 可以从 qudle 同伦不变量导出。在本文中，我们证明，对于有限四分形 X，π2(BX) 是有限生成的，并且对于连通的有限四分形 X，π2(BX) 是有限的。由此可见，有限四维的余循环不变量所跨越的空间是有限生成的。此外，我们计算一些具体问题的 π2(BX)。通过计算，具体地给出了这些问题的所有余循环不变量。此外，我们还给出了结的连通和和链接的镜像的四方同伦不变量的公式。
For a quandle X, the quandle space BX is defined, modifying the rack space of Fenn, Rourke and Sanderson (1995) [13], and the quandle homotopy invariant of links is defined in Z[π2(BX)], modifying the rack homotopy invariant of Fenn, Rourke and Sanderson (1995) [13]. It is known that the cocycle invariants introduced in Carter et al. (2005) [3], Carter et al. (2003) [5], Carter et al. (2001) [6] can be derived from the quandle homotopy invariant. In this paper, we show that, for a finite quandle X, π2(BX) is finitely generated, and that, for a connected finite quandle X, π2(BX) is finite. It follows that the space spanned by cocycle invariants for a finite quandle is finitely generated. Further, we calculate π2(BX) for some concrete quandles. From the calculation, all cocycle invariants for those quandles are concretely presented. Moreover, we show formulas of the quandle homotopy invariant for connected sum of knots and for the mirror image of links.