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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Algebraic meridians of knot groups

Author: Chichen M. Tsau
Journal: Trans. Amer. Math. Soc. 294 (1986), 733-747
MSC: Primary 57M25; Secondary 57M05
MathSciNet review: 825733
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Abstract: We propose the conjecture that every automorphism of a knot group preserves the meridian up to inverse and conjugation. We establish the conjecture for all composite knots, all torus knots, most cable knots, and at most one exception for hyperbolic knots; moreover we prove that the Property P Conjecture implies our conjecture. We also investigate hyperbolic knots in more detail, and give an example of figure-eight knot group and its automorphisms.

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Keywords: Knot manifold, knot group, presentation, automorphism of knot group, torus knot, composite knot, cable knot, hyperbolic knot, surgery manifold
Article copyright: © Copyright 1986 American Mathematical Society