### 抄録

Based on the analogies between knot theory and number theory, we study a deformation theory for SL2-representations of knot groups, following after Mazur's deformation theory of Galois representations. Firstly, by employing the pseudo-SL_{2}-representations, we prove the existence of the universal deformation of a given SL_{2}-representation of a finitely generated group π over a perfect field k whose characteristic is not 2. We then show its connection with the character scheme for SL_{2}-representations of π when k is an algebraically closed field. We investigate examples concerning Riley representations of 2-bridge knot groups and give explicit forms of the universal deformations. Finally we discuss the universal deformation of the holonomy representation of a hyperbolic knot group in connection with Thurston's theory on deformations of hyperbolic structures.

元の言語 | 英語 |
---|---|

ページ（範囲） | 67-84 |

ページ数 | 18 |

ジャーナル | Tohoku Mathematical Journal |

巻 | 69 |

発行部数 | 1 |

DOI | |

出版物ステータス | 出版済み - 3 2017 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### これを引用

_{2}-representations of knot groups.

*Tohoku Mathematical Journal*,

*69*(1), 67-84. https://doi.org/10.2748/tmj/1493172129

**On the universal deformations for SL _{2}-representations of knot groups.** / Morishita, Masanori; Takakura, Yu; Terashima, Yuji; Ueki, Jun.

研究成果: ジャーナルへの寄稿 › 記事

_{2}-representations of knot groups',

*Tohoku Mathematical Journal*, 巻. 69, 番号 1, pp. 67-84. https://doi.org/10.2748/tmj/1493172129

_{2}-representations of knot groups. Tohoku Mathematical Journal. 2017 3;69(1):67-84. https://doi.org/10.2748/tmj/1493172129

}

TY - JOUR

T1 - On the universal deformations for SL2-representations of knot groups

AU - Morishita, Masanori

AU - Takakura, Yu

AU - Terashima, Yuji

AU - Ueki, Jun

PY - 2017/3

Y1 - 2017/3

N2 - Based on the analogies between knot theory and number theory, we study a deformation theory for SL2-representations of knot groups, following after Mazur's deformation theory of Galois representations. Firstly, by employing the pseudo-SL2-representations, we prove the existence of the universal deformation of a given SL2-representation of a finitely generated group π over a perfect field k whose characteristic is not 2. We then show its connection with the character scheme for SL2-representations of π when k is an algebraically closed field. We investigate examples concerning Riley representations of 2-bridge knot groups and give explicit forms of the universal deformations. Finally we discuss the universal deformation of the holonomy representation of a hyperbolic knot group in connection with Thurston's theory on deformations of hyperbolic structures.

AB - Based on the analogies between knot theory and number theory, we study a deformation theory for SL2-representations of knot groups, following after Mazur's deformation theory of Galois representations. Firstly, by employing the pseudo-SL2-representations, we prove the existence of the universal deformation of a given SL2-representation of a finitely generated group π over a perfect field k whose characteristic is not 2. We then show its connection with the character scheme for SL2-representations of π when k is an algebraically closed field. We investigate examples concerning Riley representations of 2-bridge knot groups and give explicit forms of the universal deformations. Finally we discuss the universal deformation of the holonomy representation of a hyperbolic knot group in connection with Thurston's theory on deformations of hyperbolic structures.

UR - http://www.scopus.com/inward/record.url?scp=85016308250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85016308250&partnerID=8YFLogxK

U2 - 10.2748/tmj/1493172129

DO - 10.2748/tmj/1493172129

M3 - Article

AN - SCOPUS:85016308250

VL - 69

SP - 67

EP - 84

JO - Tohoku Mathematical Journal

JF - Tohoku Mathematical Journal

SN - 0040-8735

IS - 1

ER -