Representations of knot groups into SL<inf>n</inf>(C) and twisted Alexander polynomials

Michael Heusener, Joan Porti

Research output: Contribution to journalArticleResearchpeer-review

6 Citations (Scopus)

Abstract

©2015 Mathematical Sciences Publishers. Let Γ be the fundamental group of the exterior of a knot in the three-sphere. We study deformations of representations of 0 into SLn(C) which are the sum of two irreducible representations. For such representations we give a necessary condition, in terms of the twisted Alexander polynomial, for the existence of irreducible deformations. We also give a more restrictive sufficient condition for the existence of irreducible deformations. We also prove a duality theorem for twisted Alexander polynomials and we describe the local structure of the representation and character varieties.
Original languageEnglish
Pages (from-to)313-354
JournalPacific Journal of Mathematics
Volume277
Issue number2
DOIs
Publication statusPublished - 1 Jan 2015

Keywords

  • Character variety
  • Deformations
  • Twisted Alexander polynomial
  • Variety of representations

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