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Mosc. Math. J., 2012, Volume 12, Number 2, Pages 219–236 (Mi mmj463)  

Rational tangles and the modular group

Francesca Aicardi

ICTP, Strada Costiera, 11, I  34151 Trieste Italy

Abstract: There is a natural way to define an isomorphism between the group of transformations of isotopy classes of rational tangles and the modular group. This isomorphism allows to give a simple proof of the Conway theorem, stating the one-to-one correspondence between isotopy classes of rational tangles and rational numbers. Two other simple ways to define this isomorphisms, one of which suggested by Arnold, are also shown.

Key words and phrases: tangles, rational tangles, modular group, continued fractions, braids group, spherical braids group.

DOI: https://doi.org/10.17323/1609-4514-2012-12-2-219-236

Full text: http://www.ams.org/.../abst12-2-2012.html
References: PDF file   HTML file

Bibliographic databases:

MSC: 57M27, 20F36
Received: June 6, 2011
Language:

Citation: Francesca Aicardi, “Rational tangles and the modular group”, Mosc. Math. J., 12:2 (2012), 219–236

Citation in format AMSBIB
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\by Francesca~Aicardi
\paper Rational tangles and the modular group
\jour Mosc. Math.~J.
\yr 2012
\vol 12
\issue 2
\pages 219--236
\mathnet{http://mi.mathnet.ru/mmj463}
\crossref{https://doi.org/10.17323/1609-4514-2012-12-2-219-236}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2978753}
\zmath{https://zbmath.org/?q=an:1258.57005}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000309365900001}


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