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Here the rolling up method is explained: arxiv.org/abs/math/0607344. The problem is I could not get the from $\psi=(ab)^{11}=(ab)^5 d$ to the open book obtained by rolling up the diagram, which does not involve the curve $d$.
this is the problem I am thinking about: the problem is comparing two contact structures on the Brieskorn manifold (2,3,11). One induced by the Milnor fiber and the other one by a plumbing tree. According to a result of Ghiginni-Shoenberger:arxiv.org/abs/math/0201099 the tight contact structures on brieskorn manifold (2,3,11) are realized by two possible Legendrian realizations of the -3-knot at the tail of the plumbing. I want to check that open book from the Milnor fiber with monodromy=(ab)^11 is equivalent to the open book obtained by "rolling up" the plumbing diagram.
