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Hyperbolic covering knots - MaRDI portal

Hyperbolic covering knots (Q2571391)

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Hyperbolic covering knots
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    Hyperbolic covering knots (English)
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    1 November 2005
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    The authors have recently shown that given any knot \(k\), there are infinitely many prime knots \(k'\) whose groups admit (meridian, longitude)-preserving epimorphisms onto the group of \(k\) [J. Knot Theory Ramifications 15, No.2, 153-166 (2006; Zbl 1096.57007)]. In the paper under review this result is sharpened: the \(k'\) may be chosen to be hyperbolic knots of arbitrarily large volume, to be ribbon concordant to \(k\), and also to have the same Alexander invariant as \(k\).
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    Alexander module
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    hyperbolic knot
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    ribbon concordance
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    tangle
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