Irreducible S L (2,-metabelian representations of branched twist spins

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Abstract

An (m,n)-branched twist spin is a fibered 2-knot in S4 which is determined by a 1-knot K and coprime integers m and n. For a 1-knot, Nagasato proved that the number of conjugacy classes of irreducible SL(2, )-metabelian representations of the knot group of a 1-knot is determined by the knot determinant of the 1-knot. In this paper, we prove that the number of irreducible SL(2,)-metabelian representations of the knot group of an (m,n)-branched twist spin is determined up to conjugation by the determinant of the associated 1-knot in the orbit space by comparing a presentation of the knot group of the branched twist spin with the Lin's presentation of the knot group of the 1-knot.

Original languageEnglish
Article number1950007
JournalJournal of Knot Theory and its Ramifications
Volume28
Issue number2
DOIs
Publication statusPublished - 2019 Feb 1

Keywords

  • 2-knots
  • circle actions
  • representations

ASJC Scopus subject areas

  • Algebra and Number Theory

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