We propose a method to determine the character variety of a class J(m,n) of rational knots, which includes the twist knots. The defining polynomials depend only on the variables m and n. This answers for these classes of knots a question posed in a paper of Hilden, Lozano and Montesinos, and allows us to give an easy geometrical description of the considered character variety. Our results are obtained by using special presentations of the knot groups whose relators are palindromes.
The character variety of some classes of rational knots / Cavicchioli, Alberto; Spaggiari, Fulvia. - In: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS. - ISSN 0218-2165. - 28:9(2019), pp. 1-15. [10.1142/S021821651950055X]
The character variety of some classes of rational knots
Alberto Cavicchioli;Fulvia Spaggiari
2019
Abstract
We propose a method to determine the character variety of a class J(m,n) of rational knots, which includes the twist knots. The defining polynomials depend only on the variables m and n. This answers for these classes of knots a question posed in a paper of Hilden, Lozano and Montesinos, and allows us to give an easy geometrical description of the considered character variety. Our results are obtained by using special presentations of the knot groups whose relators are palindromes.
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