On the universal deformations for SL2-representations of knot groups

Masanori Morishita, Yu Takakura, Yuji Terashima, Jun Ueki

研究成果: ジャーナルへの寄稿記事

2 引用 (Scopus)

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-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.

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
69
発行部数1
DOI
出版物ステータス出版済み - 3 1 2017

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Knot Group
Deformation Theory
2-bridge Knot
Hyperbolic Knot
Hyperbolic Structure
Knot Theory
Hyperbolic Groups
Galois Representations
Holonomy
Finitely Generated Group
Number theory
Algebraically closed
Analogy

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

On the universal deformations for SL2-representations of knot groups. / Morishita, Masanori; Takakura, Yu; Terashima, Yuji; Ueki, Jun.

:: Tohoku Mathematical Journal, 巻 69, 番号 1, 01.03.2017, p. 67-84.

研究成果: ジャーナルへの寄稿記事

Morishita, Masanori ; Takakura, Yu ; Terashima, Yuji ; Ueki, Jun. / On the universal deformations for SL2-representations of knot groups. :: Tohoku Mathematical Journal. 2017 ; 巻 69, 番号 1. pp. 67-84.
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