Visualization of A'Campo's fibered links and unknotting operation (Q1612211)

The author gives an algorithmic method to draw the link of a ``divide''. Recall that divides were defined by N. A'Campo and are generic relative immersions in the unit disk of a finite number of 1-manifolds (i.e. intervals and circles). Following A'Campo one can associate a fibered link to a divide. The method presented by the author is applied to slalom divides to prove that the link associated to a slalom divide is arborescent. Moreover, the author gives an algorithmic construction of a Seifert surface associated to a link coming from a divide. Using these Seifert surfaces he can compute the unknotting number of a link associated to a one branch divide.