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Proceedings of the American Mathematical Society

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Twist-spun torus knots

Author: C. McA. Gordon
Journal: Proc. Amer. Math. Soc. 32 (1972), 319-322
MSC: Primary 55.20
MathSciNet review: 0288752
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Abstract: Zeeman has shown that the complement of a twist-spun knot fibres over the circle. He also proves that the group of the 5-twist-spun trefoil is just the direct product of the fundamental group of the fibre with the integers. We generalise this by showing that, for torus knots, the group of the twist-spun knot is such a direct product whenever the fibre is a homology sphere. This then suggests the question (asked by Zeeman for the case of the 5-twist-spun trefoil) as to whether there is a corresponding product structure in the geometry. We answer in the negative.

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Keywords: Twist-spinning, branched cyclic covering, fibre bundle, torus knot, peripheral element
Article copyright: © Copyright 1972 American Mathematical Society

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