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.
Fulltext:
www.ams.org/.../abst12-2-2012.html 
References
