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    A note on the generalized Matsumoto relation
    (TUBİTAK, 2017) Dalyan, Elif; Medetoğulları, Elif; Pamuk, Mehmetcik
    We 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.
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    Öğe
    Arbitrarily long factorizations in mapping class groups
    (Oxford University Press, 2015) Dalyan, Elif; Korkmaz, Mustafa; Pamuk, Mehmetcik
    Abstract. 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 manifolds