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arxiv: 0704.1432 · v1 · submitted 2007-04-11 · 🧮 math.GT

Some invariants of pretzel links

classification 🧮 math.GT
keywords linkspretzelfindgenusknotsn-pretzelpolynomialsapplications
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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.

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