We give explicit palindrome presentations of the groups of rational knots, that is, presentations with relators which read the same forwards and backwards. This answers a question posed by Hilden, Tejada and Toro in 2002. Using such presentations we obtain simple alternative proofs of some classical results concerning the Alexander polynomial of all rational knots and the character variety of certain rational knots. Finally, we derive a new recursive description of the SL(2,C) character variety of twist knots.
PALINDROME PRESENTATIONS OF RATIONAL KNOTS / Cavicchioli, Alberto; Spaggiari, Fulvia; D., Repovs. - In: JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS. - ISSN 0218-2165. - STAMPA. - 18:3(2009), pp. 343-361. [10.1142/S0218216509006963]
PALINDROME PRESENTATIONS OF RATIONAL KNOTS
CAVICCHIOLI, Alberto;SPAGGIARI, Fulvia;
2009
Abstract
We give explicit palindrome presentations of the groups of rational knots, that is, presentations with relators which read the same forwards and backwards. This answers a question posed by Hilden, Tejada and Toro in 2002. Using such presentations we obtain simple alternative proofs of some classical results concerning the Alexander polynomial of all rational knots and the character variety of certain rational knots. Finally, we derive a new recursive description of the SL(2,C) character variety of twist knots.
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