Studies on partial orders on sets of 3-manifolds defined by epimorphisms between fundamental groups.

由基本群之间的同态定义的 3 流形集上的偏序研究。

• 批准号: 21540100
• 负责人: KITANO Teruaki
• 金额: $ 2.75万
• 依托单位: Soka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540100/
• 关键词: 3次元多様体; 結び目; 基本群; 有限素体; 結び目群; 非可換表現; 全射準同型写像; metabelian表現; 写像度; Casson不変量; ねじれAlexander不変量; 半順序関係; degree

For the set of prime knots with up to 11-crossings, we determined the partial order relation defined by using meridian preserving epimorphisms between knots groups. We also proved that for any given 2-bridge knot there exists a Montesinos knot with an epimorphims which is induced by a degree zero map. Further we found pairs of a 3-bridge hyperbolic Montsinos knot and a 2-bridge hyperbolic knot which is not induced from a nonzero degree map. For any knot, there exists a infinitely many prime numbers such that there exists a non abelian representation on its knot group in 2-dimensional special linear group over a finite prime field with such a characteristic.

对于最多有 11 个交叉的素结集，我们确定了通过使用结组之间的子午线保留表同态定义的偏序关系。我们还证明，对于任何给定的 2 桥结，都存在一个带有由零度映射诱导的表态的 Montesinos 结。此外，我们还发现了成对的 3 桥双曲 Montsinos 结和 2 桥双曲结，它们不是从非零度图导出的。对于任何结，都存在无穷多个素数，使得在具有这种特性的有限素数域上的二维特殊线性群中，其结群上存在非阿贝尔表示。

项目成果

SL(2, Z/d)-represenations of a knot group and Alexander polynomial as an obstruction

SL(2, Z/d) - 结群和亚历山大多项式作为障碍的表示

• 发表时间: 2012
• 作者: M.Eudave-Munoz;K.Miyazaki;K.Motegi;Shoji Yokura;Kimihiko Motegi and Masakazu Teragaito;Takehiko Yasuda;TERUAKI KITANO
• 通讯作者: TERUAKI KITANO

Epimorphisms between knot groups

结群之间的外同态

• 发表时间: 2010
• 作者: A.Deruelle;K.Miyazaki;K.Motegi;田丸博士;芥川和雄;Y. Suyama;辻元;TERUAKI KITANO
• 通讯作者: TERUAKI KITANO

Epimorphisms between knot groups and special values of colored Jones polynomials

结群之间的同态与有色琼斯多项式的特殊值

• 发表时间: 2010
• 作者: A.Deruelle;K.Miyazaki;K.Motegi;Yoshihiko Suyama;TERUAKI KITANO
• 通讯作者: TERUAKI KITANO

Linear representations over a finite field of a knot group and the Alexander polynomial as an obstruction

结群有限域上的线性表示和作为障碍的亚历山大多项式

• 发表时间: 2011
• 作者: Akito Futaki;Hajime Ono;Guofang Wang;TERUAKI KITANO
• 通讯作者: TERUAKI KITANO

Epimorphisms between knot groups and special values of colored Jones polynomials(II)

结群间的同态与有色琼斯多项式的特殊值（二）

• 发表时间: 2011
• 作者: 新村正之;北野晃朗
• 通讯作者: 北野晃朗