On the universal deformations for SL2-representations of knot groups

Masanori Morishita, Yu Takakura, Yuji Terashima, Jun Ueki

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume69
Issue number1
DOIs
Publication statusPublished - Mar 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Fingerprint Dive into the research topics of 'On the universal deformations for SL<sub>2</sub>-representations of knot groups'. Together they form a unique fingerprint.

  • Cite this