Some invariants of Pretzel links

We show that nontrivial classical pretzel knots L (p, q, r) are hyperbolic with eight exceptions which are torus knots. We find Conway polynomials of n-pretzel links using a new computation tree. As applications, we compute the genera of n-pretzel links using these polynomials and find the basket nu...

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2007-04, Vol.75 (2), p.253-271
Hauptverfasser: Kim, Dongseok, Lee, Jaeun
Format: Artikel
Sprache:eng
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Zusammenfassung:We show that nontrivial classical pretzel knots L (p, q, r) are hyperbolic with eight exceptions which are torus knots. We find Conway polynomials of n-pretzel links using a new computation tree. As applications, we compute the genera of n-pretzel links using these polynomials and find the basket number of pretzel links by showing that the genus and the canonical genus of a pretzel link are the same.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700039198