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Öğe A note on the generalized Matsumoto relation(TUBİTAK, 2017) Dalyan, Elif; Medetoğulları, Elif; Pamuk, MehmetcikWe give an elementary proof of a relation, first discovered in its full generality by Korkmaz, in the mapping class group of a closed orientable surface. Our proof uses only the well-known relations between Dehn twists. © TÜBİTAK.Öğe Arbitrarily long factorizations in mapping class groups(Oxford University Press, 2015) Dalyan, Elif; Korkmaz, Mustafa; Pamuk, MehmetcikAbstract. On a compact oriented surface of genus g with n ? 1 boundary components, ?1, ?2, . . . , ?n, we consider positive factorizations of the boundary multitwist t?1 t?2 · · ·t?n , where t?i is the positive Dehn twist about the boundary ?i. We prove that for g ? 3, the boundary multitwist t?1 t?2 can be written as a product of arbitrarily large number of positive Dehn twists about nonseparating simple closed curves, extending a recent result of Baykur and Van Horn-Morris, who proved this result for g ? 8. This fact has immediate corollaries on the Euler characteristics of the Stein fillings of contact three manifoldsÖğe Open book decompositions of links of quotient surface singularities and support genus problem(American Institute of Mathematical Sciences, 2019) Dalyan, ElifAbstract: In this paper we write explicitly the open book decompositions of links of quotient surface singularities supporting the corresponding unique Milnor fillable contact structure. The page-genus of these Milnor open books are minimal among all Milnor open books supporting the same contact structure. We also investigate whether the Milnor genus is equal to the support genus for links of quotient surface singularities. We show that for many types of the quotient surface singularities the Milnor genus is equal to the support genus. In the remaining cases we are able to find a small upper bound for the support genus.
