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Some invariants of Pretzel links

Published online by Cambridge University Press:  17 April 2009

Dongseok Kim  and
Jaeun Lee
Dongseok Kim
Affiliation:
Department of Mathematics, Yeungnam University, Kyongsan, 712–749, Korea, e-mail: dongseok@yumail.ac.kr, julee@yu.ac.kr
Jaeun Lee
Affiliation:
Department of Mathematics, Yeungnam University, Kyongsan, 712–749, Korea, e-mail: dongseok@yumail.ac.kr, julee@yu.ac.kr
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 2 , April 2007 , pp. 253 - 271
Copyright
Copyright © Australian Mathematical Society 2007

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