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2 results

  • ASPHERICAL LABELLED ORIENTED TREES AND KNOTS

  • Günther Huck, Stephan Rosebrock
  • Journal:
    Proceedings of the Edinburgh Mathematical Society / Volume 44 / Issue 2 / June 2001
    Published online by Cambridge University Press:
    20 January 2009, pp. 285-294
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  • The question of whether ribbon-disc complements—or, equivalently, standard 2-complexes over labelled oriented trees—are aspherical is of great importance for Whitehead’s asphericity conjecture and, if solved affirmatively, would imply a combinatorial proof of the asphericity of knot complements. We present here two classes of diagrammatically reducible labelled oriented trees.

    AMS 2000 Mathematics subject classification: Primary 57M20; 20F06; 20F05; 20F32

  • Non Abelian Twisted Reidemeister Torsion for Fibered Knots

  • Jérôme Dubois
  • Journal:
    Canadian Mathematical Bulletin / Volume 49 / Issue 1 / 01 March 2006
    Published online by Cambridge University Press:
    20 November 2018, pp. 55-71
    Print publication:
    01 March 2006
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  • In this article, we give an explicit formula to compute the non abelian twisted sign-determined Reidemeister torsion of the exterior of a fibered knot in terms of its monodromy. As an application, we give explicit formulae for the non abelian Reidemeister torsion of torus knots and of the figure eight knot.