caa a22 4500 445804351 CHVBK 20180317145152.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s00453-009-9362-8 doi (NATIONALLICENCE)springer-10.1007/s00453-009-9362-8 Spiraling and Folding: The Word View [Elektronische Daten] [Marcus Schaefer, Eric Sedgwick, Daniel Štefankovič] 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 spiraling 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. Springer Science+Business Media, LLC, 2009 Curves nationallicence Surfaces nationallicence Topology nationallicence Square-free words nationallicence Thue word nationallicence Spirals nationallicence Folds nationallicence Schaefer Marcus Department of Computer Science, DePaul University, 243 South Wabash, 60604, Chicago, IL, USA aut Sedgwick Eric Department of Computer Science, DePaul University, 243 South Wabash, 60604, Chicago, IL, USA aut Štefankovič Daniel Department of Computer Science, University of Rochester, 14627, Rochester, NY, USA aut Algorithmica Springer-Verlag 60/3(2011-07-01), 609-626 0178-4617 60:3<609 2011 60 453 https://doi.org/10.1007/s00453-009-9362-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00453-009-9362-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Schaefer Marcus Department of Computer Science, DePaul University, 243 South Wabash, 60604, Chicago, IL, USA aut NATIONALLICENCE 700 1- Sedgwick Eric Department of Computer Science, DePaul University, 243 South Wabash, 60604, Chicago, IL, USA aut NATIONALLICENCE 700 1- Štefankovič Daniel Department of Computer Science, University of Rochester, 14627, Rochester, NY, USA aut NATIONALLICENCE 773 0- Algorithmica Springer-Verlag 60/3(2011-07-01), 609-626 0178-4617 60:3<609 2011 60 453 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer