Spiralling and Folding: The Word View
نویسندگان
چکیده
We show that for every n there are two simple curves on the torus intersecting at least n times without the two curves folding or spiralling with respect to each other. On the other hand, two simple curves in a punctured plane that intersect at least n times (and do not create any empty bigons) must either form a spiral of depth d or a fold of width cn/(d + 1) − 1, where c only depends on the number of punctures in the plane. The construction of the two curves on the torus involves train tracks and word equations, and the verification that the two curves do not spiral leads us to an infinite binary word based on the golden ratio which does not contain any square word ww for which |w| is even.
منابع مشابه
Folding and Spiralling: The Word View
We show that for every n there are two simple curves on the torus intersecting at least n times without the two curves folding or spiralling with respect to each other.
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