On the universal deformations for SL2-representations of knot groups

Masanori Morishita, Yu Takakura, Yuji Terashima, Jun Ueki

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3 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)67-84
Number of pages18
JournalTohoku Mathematical Journal
Issue number1
Publication statusPublished - 2017 Mar


  • Arithmetic topology
  • Character scheme
  • Deformation of a representation
  • Knot group


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